Submission #76846918

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Source Code Expand

#line 2 "/home/shogo314/cpp_include/ou-library/combinatorics.hpp"

#include <vector>
#line 2 "/home/shogo314/cpp_include/ou-library/number-theory.hpp"

#include <numeric>
#line 2 "/home/shogo314/cpp_include/ou-library/modint.hpp"

/**
 * @file modint.hpp
 * @brief 四則演算において自動で mod を取るクラス
 */

#include <iostream>
#include <utility>
#include <limits>
#include <type_traits>
#include <cstdint>
#include <cassert>

namespace detail {
    static constexpr std::uint16_t prime32_bases[] {
        15591,  2018,  166, 7429,  8064, 16045, 10503,  4399,  1949,  1295, 2776,  3620,   560,  3128,  5212,  2657,
         2300,  2021, 4652, 1471,  9336,  4018,  2398, 20462, 10277,  8028, 2213,  6219,   620,  3763,  4852,  5012,
         3185,  1333, 6227, 5298,  1074,  2391,  5113,  7061,   803,  1269, 3875,   422,   751,   580,  4729, 10239,
          746,  2951,  556, 2206,  3778,   481,  1522,  3476,   481,  2487, 3266,  5633,   488,  3373,  6441,  3344,
           17, 15105, 1490, 4154,  2036,  1882,  1813,   467,  3307, 14042, 6371,   658,  1005,   903,   737,  1887,
         7447,  1888, 2848, 1784,  7559,  3400,   951, 13969,  4304,   177,   41, 19875,  3110, 13221,  8726,   571,
         7043,  6943, 1199,  352,  6435,   165,  1169,  3315,   978,   233, 3003,  2562,  2994, 10587, 10030,  2377,
         1902,  5354, 4447, 1555,   263, 27027,  2283,   305,   669,  1912,  601,  6186,   429,  1930, 14873,  1784,
         1661,   524, 3577,  236,  2360,  6146,  2850, 55637,  1753,  4178, 8466,   222,  2579,  2743,  2031,  2226,
         2276,   374, 2132,  813, 23788,  1610,  4422,  5159,  1725,  3597, 3366, 14336,   579,   165,  1375, 10018,
        12616,  9816, 1371,  536,  1867, 10864,   857,  2206,  5788,   434, 8085, 17618,   727,  3639,  1595,  4944,
         2129,  2029, 8195, 8344,  6232,  9183,  8126,  1870,  3296,  7455, 8947, 25017,   541, 19115,   368,   566,
         5674,   411,  522, 1027,  8215,  2050,  6544, 10049,   614,   774, 2333,  3007, 35201,  4706,  1152,  1785,
         1028,  1540, 3743,  493,  4474,  2521, 26845,  8354,   864, 18915, 5465,  2447,    42,  4511,  1660,   166,
         1249,  6259, 2553,  304,   272,  7286,    73,  6554,   899,  2816, 5197, 13330,  7054,  2818,  3199,   811,
          922,   350, 7514, 4452,  3449,  2663,  4708,   418,  1621,  1171, 3471,    88, 11345,   412,  1559,   194,
    };

    static constexpr bool is_SPRP(std::uint32_t n, std::uint32_t a) noexcept {
        std::uint32_t d = n - 1;
        std::uint32_t s = 0;
        while ((d & 1) == 0) {
            ++s;
            d >>= 1;
        }
        std::uint64_t cur = 1;
        std::uint64_t pw = d;
        while (pw) {
            if (pw & 1) cur = (cur * a) % n;
            a = (static_cast<std::uint64_t>(a) * a) % n;
            pw >>= 1;
        }
        if (cur == 1) return true;
        for (std::uint32_t r = 0; r < s; ++r) {
            if (cur == n - 1) return true;
            cur = (cur * cur) % n;
        }
        return false;
    }

    // 32ビット符号なし整数の素数判定
    // 参考: M. Forisek and J. Jancina, “Fast Primality Testing for Integers That Fit into a Machine Word,” presented at the Conference on Current Trends in Theory and Practice of Informatics, 2015.
    [[nodiscard]]
    static constexpr bool is_prime32(std::uint32_t x) noexcept {
        if (x == 2 || x == 3 || x == 5 || x == 7) return true;
        if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
        if (x < 121) return (x > 1);
        std::uint64_t h = x;
        h = ((h >> 16) ^ h) * 0x45d9f3b;
        h = ((h >> 16) ^ h) * 0x45d9f3b;
        h = ((h >> 16) ^ h) & 0xff;
        return is_SPRP(x, prime32_bases[h]);
    }
}

/// @brief static_modint と dynamic_modint の実装を CRTP によって行うためのクラステンプレート
/// @tparam Modint このクラステンプレートを継承するクラス
template <class Modint>
class modint_base {
public:
    /// @brief 保持する値の型
    using value_type = std::uint32_t;

    /// @brief 0 で初期化します。
    constexpr modint_base() noexcept
        : m_value{ 0 } {}

    /// @brief @c value の剰余で初期化します。
    /// @param value 初期化に使う値
    template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral> && std::is_signed_v<SignedIntegral>>* = nullptr>
    constexpr modint_base(SignedIntegral value) noexcept
        : m_value{ static_cast<value_type>((static_cast<long long>(value) % Modint::mod() + Modint::mod()) % Modint::mod()) } {}

    /// @brief @c value の剰余で初期化します。
    /// @param value 初期化に使う値
    template <class UnsignedIntegral, std::enable_if_t<std::is_integral_v<UnsignedIntegral> && std::is_unsigned_v<UnsignedIntegral>>* = nullptr>
    constexpr modint_base(UnsignedIntegral value) noexcept
        : m_value{ static_cast<value_type>(value % Modint::mod()) } {}

    /// @brief 保持している値を取得します。
    /// @return 保持している値
    [[nodiscard]]
    constexpr value_type value() const noexcept {
        return m_value;
    }

    /// @brief 保持している値をインクリメントして、剰余を取ります。
    /// @return @c *this
    constexpr Modint& operator++() noexcept {
        ++m_value;
        if (m_value == Modint::mod()) {
            m_value = 0;
        }
        return static_cast<Modint&>(*this);
    }

    /// @brief 保持している値をインクリメントして、剰余を取ります。
    /// @return @c *this
    constexpr Modint operator++(int) noexcept {
        auto x = static_cast<const Modint&>(*this);
        ++*this;
        return x;
    }

    /// @brief 保持している値をデクリメントして、剰余を取ります。
    /// @return @c *this
    constexpr Modint& operator--() noexcept {
        if (m_value == 0) {
            m_value = Modint::mod();
        }
        --m_value;
        return static_cast<Modint&>(*this);
    }

    /// @brief 保持している値をデクリメントして、剰余を取ります。
    /// @return @c *this
    constexpr Modint operator--(int) noexcept {
        auto x = static_cast<const Modint&>(*this);
        --*this;
        return x;
    }

    /// @brief 保持している値に @c x の持つ値を足して、剰余を取ります。
    /// @param x 足す数
    /// @return @c *this
    constexpr Modint& operator+=(const Modint& x) noexcept {
        m_value += x.m_value;
        if (m_value >= Modint::mod()) {
            m_value -= Modint::mod();
        }
        return static_cast<Modint&>(*this);
    }

    /// @brief 保持している値から @c x の持つ値を引いて、剰余を取ります。
    /// @param x 引く数
    /// @return @c *this
    constexpr Modint& operator-=(const Modint& x) noexcept {
        m_value -= x.m_value;
        if (m_value >= Modint::mod()) {
            m_value += Modint::mod();
        }
        return static_cast<Modint&>(*this);
    }

    /// @brief 保持している値に @c x の持つ値を掛けて、剰余を取ります。
    /// @param x 掛ける数
    /// @return @c *this
    constexpr Modint& operator*=(const Modint& x) noexcept {
        m_value = static_cast<value_type>(static_cast<std::uint64_t>(m_value) * x.m_value % Modint::mod());
        return static_cast<Modint&>(*this);
    }

    /// @brief 保持している値を @c x の持つ値で割って、剰余を取ります。
    /// @remark 時間計算量： @f$O(\log x)@f$
    /// @param x 割る数
    /// @return @c *this
    constexpr Modint& operator/=(const Modint& x) noexcept {
        return *this *= x.inv();
    }

    /// @brief 自身のコピーを返します。
    /// @return @c *this
    [[nodiscard]]
    constexpr Modint operator+() const noexcept {
        return static_cast<const Modint&>(*this);
    }

    /// @brief 自身の反数を返します。
    /// @return 自身の反数
    [[nodiscard]]
    constexpr Modint operator-() const noexcept {
        return 0 - static_cast<const Modint&>(*this);
    }

    /// @brief 自身の @c n 乗を返します。
    /// @remark 時間計算量： @f$O(\log n)@f$
    /// @param n 指数
    /// @return 自身の @c n 乗
    [[nodiscard]]
    constexpr Modint pow(unsigned long long n) const noexcept {
        Modint x = 1;
        Modint y = static_cast<const Modint&>(*this);
        while (n) {
            if (n & 1) {
                x *= y;
            }
            y *= y;
            n >>= 1;
        }
        return x;
    }

    /// @brief 自身の逆数を返します。
    /// @remark 時間計算量： @f$O(\log value)@f$
    /// @return 自身の逆数
    [[nodiscard]]
    constexpr Modint inv() const noexcept {
        long long a = Modint::mod();
        long long b = m_value;
        long long x = 0;
        long long y = 1;
        while (b) {
            auto t = a / b;
            auto u = a - t * b;
            a = b;
            b = u;
            u = x - t * y;
            x = y;
            y = u;
        }
        assert(a == 1 && "The inverse element does not exist.");
        x %= Modint::mod();
        if (x < 0) {
            x += Modint::mod();
        }
        return x;
    }

    /// @brief @c x に @c y を足したオブジェクトを返します。
    /// @param x 足される数
    /// @param y 足す数
    /// @return @c x に @c y を足したオブジェクト
    [[nodiscard]]
    friend constexpr Modint operator+(const Modint& x, const Modint& y) noexcept {
        return std::move(Modint{ x } += y);
    }

    /// @brief @c x から @c y を引いたオブジェクトを返します。
    /// @param x 引かれる数
    /// @param y 引く数
    /// @return @c x から @c y を引いたオブジェクト
    [[nodiscard]]
    friend constexpr Modint operator-(const Modint& x, const Modint& y) noexcept {
        return std::move(Modint{ x } -= y);
    }

    /// @brief @c x に @c y を掛けたオブジェクトを返します。
    /// @param x 掛けられる数
    /// @param y 掛ける数
    /// @return @c x に @c y を掛けたオブジェクト
    [[nodiscard]]
    friend constexpr Modint operator*(const Modint& x, const Modint& y) noexcept {
        return std::move(Modint{ x } *= y);
    }

    /// @brief @c x を @c y で割ったオブジェクトを返します。
    /// @param x 割られる数
    /// @param y 割る数
    /// @return @c x を @c y で割ったオブジェクト
    [[nodiscard]]
    friend constexpr Modint operator/(const Modint& x, const Modint& y) noexcept {
        return std::move(Modint{ x } /= y);
    }

    /// @brief @c x と @c y の保持する値が等しいかどうかを調べます。
    /// @return @c x と @c y の保持する値が等しければ @c true 、そうでなければ @c false
    [[nodiscard]]
    friend constexpr bool operator==(const Modint& x, const Modint& y) noexcept {
        return x.m_value == y.m_value;
    }

    /// @brief @c x と @c y の保持する値が等しくないかどうかを調べます。
    /// @return @c x と @c y の保持する値が等しければ @c false 、そうでなければ @c true
    [[nodiscard]]
    friend constexpr bool operator!=(const Modint& x, const Modint& y) noexcept {
        return not (x == y);
    }

    /// @brief 入力ストリームから符号付き整数を読み取り、 @c x に格納します。
    /// @tparam CharT 入力ストリームの文字型
    /// @tparam Traits 入力ストリームの文字トレイト
    /// @param is 入力ストリーム
    /// @param x 入力を受け取るオブジェクト
    /// @return @c is
    template <class CharT, class Traits>
    friend std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, Modint& x) {
        long long tmp;
        is >> tmp;
        x = tmp;
        return is;
    }

    /// @brief 出力ストリームに @c x の保持する値を出力します。
    /// @tparam CharT 出力ストリームの文字型
    /// @tparam Traits 出力ストリームの文字トレイト
    /// @param os 出力ストリーム
    /// @param x 出力するオブジェクト
    /// @return @c os
    template <class CharT, class Traits>
    friend std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const Modint& x) {
        os << x.value();
        return os;
    }

protected:
    value_type m_value;
};

/// @brief コンパイル時に法が決まるとき、四則演算において自動で mod を取るクラス
/// @tparam Mod 法
template <std::uint32_t Mod>
class static_modint : public modint_base<static_modint<Mod>> {
    static_assert(Mod > 0 && Mod <= std::numeric_limits<std::uint32_t>::max() / 2);

private:
    using base_type = modint_base<static_modint<Mod>>;

public:
    using typename base_type::value_type;

    /// @brief 法を取得します。
    /// @return 法
    [[nodiscard]]
    static constexpr value_type mod() noexcept {
        return Mod;
    }

    /// @brief 0 で初期化します。
    constexpr static_modint() noexcept
        : base_type{} {}

    /// @brief @c value の剰余で初期化します。
    /// @param value 初期化に使う値
    template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral>>* = nullptr>
    constexpr static_modint(SignedIntegral value) noexcept
        : base_type{value} {}

    /// @brief 自身の逆数を返します。
    /// @remark 時間計算量： @f$O(\log value)@f$
    /// @return 自身の逆数
    [[nodiscard]]
    constexpr static_modint inv() const noexcept {
        if constexpr (detail::is_prime32(Mod)) {
            assert(this->m_value != 0 && "The inverse element of zero does not exist.");
            return this->pow(Mod - 2);
        }
        else {
            return base_type::inv();
        }
    }
};

/// @brief 実行時に法が決まるとき、四則演算において自動で mod を取るクラス
/// @tparam ID このIDごとに法を設定することができます
template <int ID>
class dynamic_modint : public modint_base<dynamic_modint<ID>> {
private:
    using base_type = modint_base<dynamic_modint<ID>>;

public:
    using typename base_type::value_type;

    /// @brief 法を取得します。
    /// @return 法
    [[nodiscard]]
    static value_type mod() noexcept {
        return modulus;
    }

    /// @brief 法を設定します。
    /// @param m 新しい法
    static void set_mod(value_type m) noexcept {
        assert(m > 0 && m <= std::numeric_limits<value_type>::max() / 2);
        modulus = m;
    }

    /// @brief 0 で初期化します。
    constexpr dynamic_modint() noexcept
        : base_type{} {}

    /// @brief @c value の剰余で初期化します。
    /// @param value 初期化に使う値
    template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral>>* = nullptr>
    constexpr dynamic_modint(SignedIntegral value) noexcept
        : base_type{value} {}

private:
    inline static value_type modulus = 998244353;
};

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
#line 6 "/home/shogo314/cpp_include/ou-library/number-theory.hpp"

/**
 * @brief a^(-1) mod MODを返す
 * @param a long long
 * @param MOD long long
 * @return long long
 */
long long modinv(long long a, long long MOD) {
    long long b = MOD, u = 1, v = 0;
    while (b) {
        long long t = a / b;
        a -= t * b; std::swap(a, b);
        u -= t * v; std::swap(u, v);
    }
    u %= MOD; 
    if (u < 0) u += MOD;
    return u;
}

/**
 * @brief a^n mod MODを返す
 * @param a long long
 * @param n long long
 * @param MOD long long
 * @return long long
 */
long long modpow(long long a, long long n, long long MOD) {
    long long res = 1;
    a %= MOD;
    if(n < 0) {
        n = -n;
        a = modinv(a, MOD);
    }
    while (n > 0) {
        if (n & 1) res = res * a % MOD;
        a = a * a % MOD;
        n >>= 1;
    }
    return res;
}

/**
 * @brief 2式の連立合同式を、mが互いに素になるように変形する
 * @param r1 long long
 * @param m1 long long
 * @param r2 long long
 * @param m2 long long
 * @note 矛盾する場合、r1 = r2 = m1 = m2 = -1となる
 */
void coprimize_simulaneous_congruence_equation(long long& r1, long long& m1, long long& r2, long long& m2) {
    long long g = std::gcd(m1, m2);
    if((r2 - r1) % g != 0) {
        r1 = r2 = m1 = m2 = -1;
        return;
    }
    m1 /= g, m2 /= g;
    long long gi = std::gcd(g, m1);
    long long gj = g / gi;
    do {
        g = std::gcd(gi, gj);
        gi *= g, gj /= g;
    } while(g != 1);
    m1 *= gi, m2 *= gj;
    r1 %= m1, r2 %= m2;
}

/**
 * @brief 連立合同式を解く
 * @param r vector<long long> 余りの配列
 * @param m vector<long long> modの配列
 * @return std::pair<long long, long long> (解, LCM) 解なしのときは{-1, -1}
 */
std::pair<long long, long long> crt(const std::vector<long long>& r, const std::vector<long long>& m) {
    assert(r.size() == m.size());
    if(r.size() == 0) return {0, 1};
    int n = (int)r.size();
    long long m_lcm = m[0];
    long long ans = r[0] % m[0];
    for (int i = 1; i < n; i++) {
        long long rr = r[i] % m[i], mm = m[i];
        coprimize_simulaneous_congruence_equation(ans, m_lcm, rr, mm);
        if(m_lcm == -1) return {-1, -1};
        long long t = ((rr - ans) * modinv(m_lcm, mm)) % mm;
        if(t < 0) t += mm;
        ans += t * m_lcm;
        m_lcm *= mm;
    }
    return {ans, m_lcm};
}

/**
 * @brief 連立合同式の最小の非負整数解 % MODを求める
 * @param r vector<long long> 余りの配列
 * @param m vector<long long> modの配列
 * @param MOD long long
 * @return std::pair<long long, long long> (最小解 % MOD, LCM % MOD) 解なしのときは{-1, -1}
 */
std::pair<long long, long long> crt(const std::vector<long long>& r, const std::vector<long long>& m, long long MOD) {
    assert(r.size() == m.size());
    if(r.size() == 0) return {0, 1};
    int n = (int)r.size();
    std::vector<long long> r2 = r, m2 = m;
    // mを互いに素にする
    for(int i = 1; i < n; i++) {
        for(int j = 0; j < i; j++) {
            coprimize_simulaneous_congruence_equation(r2[i], m2[i], r2[j], m2[j]);
            if(m2[i] == -1) return {-1, -1};
        }
    }

    m2.push_back(MOD);
    std::vector<long long> prod(n+1, 1); // m2[0] * ... * m2[i - 1] mod m2[i]
    std::vector<long long> x(n+1, 0); // i番目までの解 mod m2[i]
    for(int i = 0; i < n; i++) {
        long long t = (r2[i] - x[i]) * modinv(prod[i], m2[i]) % m2[i];
        if(t < 0) t += m2[i];
        for(int j = i + 1; j <= n; j++) {
            (x[j] += t * prod[j]) %= m2[j];
            (prod[j] *= m2[i]) %= m2[j];
        }
    }
    return {x[n], prod[n]};
}

/**
 * @brief 畳み込み
 */
namespace NTT {
    /**
     * @brief 原子根
     * @param MOD int
     * @return int
     */
    int calc_primitive_root(int MOD) {
        if (MOD == 2) return 1;
        if (MOD == 167772161) return 3;
        if (MOD == 469762049) return 3;
        if (MOD == 754974721) return 11;
        if (MOD == 998244353) return 3;
        int divs[20] = {};
        divs[0] = 2;
        int cnt = 1;
        long long x = (MOD - 1) >> 1;
        while (x % 2 == 0) x >>= 1;
        for (long long i = 3; i * i <= x; i += 2) {
            if (x % i == 0) {
                divs[cnt ++] = i;
                while (x % i == 0) x /= i;
            }
        }
        if (x > 1) divs[cnt++] = x;
        for (int g = 2;; ++ g) {
            bool ok = true;
            for (int i = 0; i < cnt; i++) {
                if (modpow(g, (MOD - 1) / divs[i], MOD) == 1) {
                    ok = false;
                    break;
                }
            }
            if (ok) return g;
        }
    }

    /**
     * @brief 畳み込みのサイズを2のべき乗にする
     */
    int get_fft_size(int N, int M) {
        int size_a = 1, size_b = 1;
        while (size_a < N) size_a <<= 1;
        while (size_b < M) size_b <<= 1;
        return std::max(size_a, size_b) << 1;
    }

    /**
     * @brief NTT
     */
    template<class mint> void trans(std::vector<mint>& v, bool inv = false) {
        if (v.empty()) return;
        int N = (int) v.size();
        int MOD = v[0].mod();
        int PR = calc_primitive_root(MOD);
        static bool first = true;
        static std::vector<long long> vbw(30), vibw(30);
        if (first) {
            first = false;
            for (int k = 0; k < 30; ++ k) {
                vbw[k] = modpow(PR, (MOD - 1) >> (k + 1), MOD);
                vibw[k] = modinv(vbw[k], MOD);
            }
        }
        for (int i = 0, j = 1; j < N - 1; ++ j) {
            for (int k = N >> 1; k > (i ^= k); k >>= 1);
            if (i > j) std::swap(v[i], v[j]);
        }
        for (int k = 0, t = 2; t <= N; ++ k, t <<= 1) {
            long long bw = vbw[k];
            if (inv) bw = vibw[k];
            for (int i = 0; i < N; i += t) {
                mint w = 1;
                for (int j = 0; j < (t >> 1); ++ j) {
                    int j1 = i + j, j2 = i + j + (t >> 1);
                    mint c1 = v[j1], c2 = v[j2] * w;
                    v[j1] = c1 + c2;
                    v[j2] = c1 - c2;
                    w *= bw;
                }
            }
        }
        if (inv) {
            long long invN = modinv(N, MOD);
            for (int i = 0; i < N; ++ i) v[i] = v[i] * invN;
        }
    }

    static constexpr int MOD0 = 754974721;
    static constexpr int MOD1 = 167772161;
    static constexpr int MOD2 = 469762049;
    using mint0 = static_modint<MOD0>;
    using mint1 = static_modint<MOD1>;
    using mint2 = static_modint<MOD2>;
    static const mint1 imod0 = 95869806; // modinv(MOD0, MOD1);
    static const mint2 imod1 = 104391568; // modinv(MOD1, MOD2);
    static const mint2 imod01 = 187290749; // imod1 / MOD0;

    /**
     * @brief 配列のサイズが小さいときの畳み込み
     * @param T mint, long long
     * @param A vector<T>
     * @param B vector<T>
     * @return vector<T>
     */
    template<class T> std::vector<T> naive
    (const std::vector<T>& A, const std::vector<T>& B) {
        if (A.empty() || B.empty()) return {};
        int N = (int) A.size(), M = (int) B.size();
        std::vector<T> res(N + M - 1);
        for (int i = 0; i < N; ++ i)
            for (int j = 0; j < M; ++ j)
                res[i + j] += A[i] * B[j];
        return res;
    }
};

/**
 * @brief modintの畳み込み
 * @param A vector<mint>
 * @param B vector<mint>
 * @return vector<mint>
 */
template<class mint> std::vector<mint> convolution
(const std::vector<mint>& A, const std::vector<mint>& B) {
    if (A.empty() || B.empty()) return {};
    int N = (int) A.size(), M = (int) B.size();
    if (std::min(N, M) < 30) return NTT::naive(A, B);
    int MOD = A[0].mod();
    int size_fft = NTT::get_fft_size(N, M);
    if (MOD == 998244353) {
        std::vector<mint> a(size_fft), b(size_fft), c(size_fft);
        for (int i = 0; i < N; ++i) a[i] = A[i];
        for (int i = 0; i < M; ++i) b[i] = B[i];
        NTT::trans(a), NTT::trans(b);
        std::vector<mint> res(size_fft);
        for (int i = 0; i < size_fft; ++i) res[i] = a[i] * b[i];
        NTT::trans(res, true);
        res.resize(N + M - 1);
        return res;
    }
    std::vector<NTT::mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
    std::vector<NTT::mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
    std::vector<NTT::mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
    for (int i = 0; i < N; ++ i) {
        a0[i] = A[i].value();
        a1[i] = A[i].value();
        a2[i] = A[i].value();
    }
    for (int i = 0; i < M; ++ i) {
        b0[i] = B[i].value();
        b1[i] = B[i].value();
        b2[i] = B[i].value();
    }
    NTT::trans(a0), NTT::trans(a1), NTT::trans(a2), 
    NTT::trans(b0), NTT::trans(b1), NTT::trans(b2);
    for (int i = 0; i < size_fft; ++i) {
        c0[i] = a0[i] * b0[i];
        c1[i] = a1[i] * b1[i];
        c2[i] = a2[i] * b2[i];
    }
    NTT::trans(c0, true), NTT::trans(c1, true), NTT::trans(c2, true);
    static const mint mod0 = NTT::MOD0, mod01 = mod0 * NTT::MOD1;
    std::vector<mint> res(N + M - 1);
    for (int i = 0; i < N + M - 1; ++ i) {
        int y0 = c0[i].value();
        int y1 = (NTT::imod0 * (c1[i] - y0)).value();
        int y2 = (NTT::imod01 * (c2[i] - y0) - NTT::imod1 * y1).value();
        res[i] = mod01 * y2 + mod0 * y1 + y0;
    }
    return res;
}

/**
 * @brief long longの畳み込み
 * @param A vector<long long>
 * @param B vector<long long>
 * @return vector<long long>
 */
std::vector<long long> convolution_ll
(const std::vector<long long>& A, const std::vector<long long>& B) {
    if (A.empty() || B.empty()) return {};
    int N = (int) A.size(), M = (int) B.size();
    if (std::min(N, M) < 30) return NTT::naive(A, B);
    int size_fft = NTT::get_fft_size(N, M);
    std::vector<NTT::mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
    std::vector<NTT::mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
    std::vector<NTT::mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
    for (int i = 0; i < N; ++ i) {
        a0[i] = A[i];
        a1[i] = A[i];
        a2[i] = A[i];
    }
    for (int i = 0; i < M; ++ i) {
        b0[i] = B[i];
        b1[i] = B[i];
        b2[i] = B[i];
    }
    NTT::trans(a0), NTT::trans(a1), NTT::trans(a2), 
    NTT::trans(b0), NTT::trans(b1), NTT::trans(b2);
    for (int i = 0; i < size_fft; ++ i) {
        c0[i] = a0[i] * b0[i];
        c1[i] = a1[i] * b1[i];
        c2[i] = a2[i] * b2[i];
    }
    NTT::trans(c0, true), NTT::trans(c1, true), NTT::trans(c2, true);
    static const long long mod0 = NTT::MOD0, mod01 = mod0 * NTT::MOD1;
    static const __int128_t mod012 = (__int128_t)mod01 * NTT::MOD2;
    std::vector<long long> res(N + M - 1);
    for (int i = 0; i < N + M - 1; ++ i) {
        int y0 = c0[i].value();
        int y1 = (NTT::imod0 * (c1[i] - y0)).value();
        int y2 = (NTT::imod01 * (c2[i] - y0) - NTT::imod1 * y1).value();
        __int128_t tmp = (__int128_t)mod01 * y2 + (__int128_t)mod0 * y1 + y0;
        if(tmp < (mod012 >> 1)) res[i] = tmp;
        else res[i] = tmp - mod012;
    }
    return res;
}
#line 5 "/home/shogo314/cpp_include/ou-library/combinatorics.hpp"

/**
 * @brief 組み合わせ
 */
template <typename Modint>
class Combination {
    static std::vector<Modint> fact, inv_fact;

public:
    /**
     * @brief n までの階乗とその逆元を前計算する
     * @param n
     * @note O(n) 必要になったら呼び出されるが、予め大きなnに対して呼び出しておくことで逆元の直接計算を減らせる
     */
    inline static void extend(int n) {
        int m = fact.size();
        if (n < m) return;
        fact.resize(n + 1);
        inv_fact.resize(n + 1);
        for (int i = m; i <= n; ++i) {
            fact[i] = fact[i - 1] * i;
        }
        inv_fact[n] = fact[n].inv();
        for (int i = n; i > m; --i) {
            inv_fact[i - 1] = inv_fact[i] * i;
        }
    }
    
    /**
     * @brief n の階乗を返す
     * @param n
     * @return n!
     * @note extend(n), O(1)
     */
    inline static Modint factorial(int n) {
        extend(n);
        return fact[n];
    }
    /**
     * @brief n の階乗の逆元を返す
     * @param n
     * @return n!^-1
     * @note extend(n), O(1)
     */
    inline static Modint inverse_factorial(int n) {
        extend(n);
        return inv_fact[n];
    }
    /**
     * @brief n の逆元を返す
     * @param n
     * @return n^-1
     * @note extend(n), O(1)
     */
    inline static Modint inverse(int n) {
        extend(n);
        return inv_fact[n] * fact[n - 1];
    }

    /**
     * @brief nPr を返す
     * @param n
     * @param r
     * @return nPr
     * @note extend(n), O(1)
     */
    inline static Modint P(int n, int r) {
        if (r < 0 || n < r) return 0;
        extend(n);
        return fact[n] * inv_fact[n - r];
    }
    /**
     * @brief nCr を返す
     * @param n
     * @param r
     * @return nCr
     * @note extend(n), O(1)
     */
    inline static Modint C(int n, int r) {
        if (r < 0 || n < r) return 0;
        extend(n);
        return fact[n] * inv_fact[r] * inv_fact[n - r];
    }
    /**
     * @brief nHr を返す
     * @param n
     * @param r
     * @return nHr
     * @note extend(n+r-1), O(1)
     */
    inline static Modint H(int n, int r) {
        if (n < 0 || r < 0) return 0;
        if (n == 0 && r == 0) return 1;
        return C(n + r - 1, r);
    }

    /**
     * @brief nPr を定義どおり計算する
     * @param n
     * @param r
     * @return nPr
     * @note O(r)
     */
    inline static Modint P_loop(long long n, int r) {
        if (r < 0 || n < r) return 0;
        Modint res = 1;
        for (int i = 0; i < r; ++i) {
            res *= n - i;
        }
        return res;
    }
    /**
     * @brief nCr を定義どおり計算する
     * @param n
     * @param r
     * @return nCr
     * @note O(min(r, n-r))
     */
    inline static Modint C_loop(long long n, long long r) {
        if (r < 0 || n < r) return 0;
        if(r > n - r) r = n - r;
        extend(r);
        return P_loop(n, r) * inv_fact[r];
    }
    /**
     * @brief nHr を定義どおり計算する
     * @param n
     * @param r
     * @return nHr
     * @note O(r)
     */
    inline static Modint H_loop(long long n, long long r) {
        if (n < 0 || r < 0) return 0;
        if (n == 0 && r == 0) return 1;
        return C_loop(n + r - 1, r);
    }

    /**
     * @brief nCr を Lucas の定理を用いて計算する
     * @param n
     * @param r
     * @return nCr
     * @note expand(Mod), O(log(r))
     */
    inline static Modint C_lucas(long long n, long long r) {
        if (r < 0 || n < r) return 0;
        if (r == 0 || n == r) return 1;
        Modint res = 1;
        while(r > 0) {
            int ni = n % Modint::mod(), ri = r % Modint::mod();
            if (ni < ri) return 0;
            res *= C(ni, ri);
            n /= Modint::mod();
            r /= Modint::mod();
        }
        return res;
    }
};

template <typename Modint>
std::vector<Modint> Combination<Modint>::fact{1, 1};
template <typename Modint>
std::vector<Modint> Combination<Modint>::inv_fact{1, 1};

/**
 * @brief mod p^q での二項係数を求める構造
 * @note 前計算O(p^q) 参考: https://nyaannyaan.github.io/library/modulo/arbitrary-mod-binomial.hpp
 */
struct CombinationPQ {
    int p, q;
    int pq;
    std::vector<int> fact_p, inv_fact_p;
    int delta;
    CombinationPQ(int p, int q) : p(p), q(q) {
        pq = 1;
        for(int i = 0; i < q; i++) pq *= p;
        fact_p.resize(pq);
        fact_p[0] = 1;
        for(int i = 1; i < pq; i++) {
            if(i % p == 0) fact_p[i] = fact_p[i - 1];
            else fact_p[i] = (long long)fact_p[i - 1] * i % pq;
        }
        inv_fact_p.resize(pq);
        inv_fact_p[pq - 1] = modinv(fact_p[pq - 1], pq);
        for(int i = pq - 1; i > 0; i--) {
            if(i % p == 0) inv_fact_p[i - 1] = inv_fact_p[i];
            else inv_fact_p[i - 1] = (long long)inv_fact_p[i] * i % pq;
        }
        if(p == 2 && q >= 3) delta = 1;
        else delta = -1;
    }
    /**
     * @brief nCr mod p^q を返す
     * @param n long long
     * @param r long long
     * @return nCr mod p^q
     * @note O(log(n))
     */
    int C(long long n, long long r) {
        if(r < 0 || n < r) return 0;
        long long m = n - r;
        int ans = 1;
        std::vector<int> epsilon;
        while(n > 0) {
            ans = (long long)ans * fact_p[n % pq] % pq;
            ans = (long long)ans * inv_fact_p[m % pq] % pq;
            ans = (long long)ans * inv_fact_p[r % pq] % pq;
            n /= p;
            m /= p;
            r /= p;
            epsilon.push_back(n - m - r);
        }
        if(delta == -1 && epsilon.size() >= q && accumulate(epsilon.begin()+q-1, epsilon.end(), 0) % 2 == 1) ans = pq - ans;
        if(ans == pq) ans = 0;
        int e = accumulate(epsilon.begin(), epsilon.end(), 0);
        if(e >= q) ans = 0;
        else {
            for(int i = 0; i < e; i++) {
                ans = (long long)ans * p % pq;
            }
        }
        return ans;
    }
};
#line 2 "/home/shogo314/cpp_include/sh-library/base/all"
#include <bits/stdc++.h>
#line 5 "/home/shogo314/cpp_include/sh-library/base/container_func.hpp"
#include <initializer_list>
#line 5 "/home/shogo314/cpp_include/sh-library/base/traits.hpp"

#define HAS_METHOD(func_name)                                                              \
    namespace detail {                                                                     \
    template <class T, class = void>                                                       \
    struct has_##func_name##_impl : std::false_type {};                                    \
    template <class T>                                                                     \
    struct has_##func_name##_impl<T, std::void_t<decltype(std::declval<T>().func_name())>> \
        : std::true_type {};                                                               \
    }                                                                                      \
    template <class T>                                                                     \
    struct has_##func_name : detail::has_##func_name##_impl<T>::type {};                   \
    template <class T>                                                                     \
    inline constexpr bool has_##func_name##_v = has_##func_name<T>::value;

#define HAS_METHOD_ARG(func_name)                                                                              \
    namespace detail {                                                                                         \
    template <class T, typename U, class = void>                                                               \
    struct has_##func_name##_impl : std::false_type {};                                                        \
    template <class T, typename U>                                                                             \
    struct has_##func_name##_impl<T, U, std::void_t<decltype(std::declval<T>().func_name(std::declval<U>()))>> \
        : std::true_type {};                                                                                   \
    }                                                                                                          \
    template <class T, typename U>                                                                             \
    struct has_##func_name : detail::has_##func_name##_impl<T, U>::type {};                                    \
    template <class T, typename U>                                                                             \
    inline constexpr bool has_##func_name##_v = has_##func_name<T, U>::value;

HAS_METHOD(repr)
HAS_METHOD(type_str)
HAS_METHOD(initializer_str)
HAS_METHOD(max)
HAS_METHOD(min)
HAS_METHOD(reversed)
HAS_METHOD(sorted)
HAS_METHOD(sum)
HAS_METHOD(product)
HAS_METHOD(product_xor)
HAS_METHOD_ARG(count)
HAS_METHOD_ARG(find)
HAS_METHOD_ARG(lower_bound)
HAS_METHOD_ARG(upper_bound)

#define ENABLE_IF_T_IMPL(expr) std::enable_if_t<expr, std::nullptr_t> = nullptr
#define ENABLE_IF_T(...) ENABLE_IF_T_IMPL((__VA_ARGS__))

template <class C>
using mem_value_type = typename C::value_type;
template <class C>
using mem_difference_type = typename C::difference_type;

namespace detail {
template <class T, class = void>
struct is_sorted_container_impl : std::false_type {};
template <class T>
struct is_sorted_container_impl<std::set<T>> : std::true_type {};
template <class T>
struct is_sorted_container_impl<std::multiset<T>> : std::true_type {};
}  // namespace detail
template <class T>
struct is_sorted_container : detail::is_sorted_container_impl<T>::type {};
template <class T>
inline constexpr bool is_sorted_container_v = is_sorted_container<T>::value;
#line 9 "/home/shogo314/cpp_include/sh-library/base/container_func.hpp"

#define METHOD_EXPAND(func)                                        \
    template <typename T, ENABLE_IF_T(has_##func##_v<T>)>          \
    inline constexpr auto func(const T &t) -> decltype(t.func()) { \
        return t.func();                                           \
    }

#define METHOD_AND_FUNC_ARG_EXPAND(func)                                     \
    template <typename T, typename U, ENABLE_IF_T(has_##func##_v<T, U>)>     \
    inline constexpr auto func(const T &t, const U &u)                       \
        -> decltype(t.func(u)) {                                             \
        return t.func(u);                                                    \
    }                                                                        \
    template <typename T, typename U, ENABLE_IF_T(not has_##func##_v<T, U>)> \
    inline constexpr auto func(const T &t, const U &u)                       \
        -> decltype(std::func(t.begin(), t.end(), u)) {                      \
        return std::func(t.begin(), t.end(), u);                             \
    }

METHOD_EXPAND(reversed)
template <class C, ENABLE_IF_T(not has_reversed_v<C>)>
inline constexpr C reversed(C t) {
    std::reverse(t.begin(), t.end());
    return t;
}

METHOD_EXPAND(sorted)
template <class C, ENABLE_IF_T(not has_sorted_v<C>)>
inline constexpr C sorted(C t, bool reverse = false) {
    std::sort(t.begin(), t.end());
    if (reverse) std::reverse(t.begin(), t.end());
    return t;
}
template <class C, class F, ENABLE_IF_T(not has_sorted_v<C> and std::is_invocable_r_v<bool, F, mem_value_type<C>, mem_value_type<C>>)>
inline constexpr C sorted(C t, F f) {
    std::sort(t.begin(), t.end(), f);
    return t;
}

template <class C>
inline constexpr void sort(C &t, bool reverse = false) {
    std::sort(t.begin(), t.end());
    if (reverse) std::reverse(t.begin(), t.end());
}
template <class C, class F, ENABLE_IF_T(std::is_invocable_r_v<bool, F, mem_value_type<C>, mem_value_type<C>>)>
inline constexpr void sort(C &t, F f) {
    std::sort(t.begin(), t.end(), f);
}
template <class C, class F, ENABLE_IF_T(std::is_invocable_v<F, mem_value_type<C>>)>
inline constexpr void sort_by_key(C &t, F f) {
    std::sort(t.begin(), t.end(), [&](const mem_value_type<C> &left, const mem_value_type<C> &right) {
        return f(left) < f(right);
    });
}

template <class C>
inline constexpr void reverse(C &t) {
    std::reverse(t.begin(), t.end());
}

METHOD_EXPAND(max)
template <class C, ENABLE_IF_T(not has_max_v<C> and is_sorted_container_v<C>)>
inline constexpr mem_value_type<C> max(const C &v) {
    assert(v.begin() != v.end());
    return *v.rbegin();
}
template <class C, ENABLE_IF_T(not has_max_v<C> and not is_sorted_container_v<C>)>
inline constexpr mem_value_type<C> max(const C &v) {
    assert(v.begin() != v.end());
    return *std::max_element(v.begin(), v.end());
}
template <typename T>
inline constexpr T max(const std::initializer_list<T> &v) {
    return std::max(v);
}

METHOD_EXPAND(min)
template <class C, ENABLE_IF_T(not has_max_v<C> and is_sorted_container_v<C>)>
inline constexpr mem_value_type<C> min(const C &v) {
    assert(v.begin() != v.end());
    return *v.begin();
}
template <class C, ENABLE_IF_T(not has_max_v<C> and not is_sorted_container_v<C>)>
inline constexpr mem_value_type<C> min(const C &v) {
    assert(v.begin() != v.end());
    return *std::min_element(v.begin(), v.end());
}
template <typename T>
inline constexpr T min(const std::initializer_list<T> &v) {
    return std::min(v);
}

METHOD_EXPAND(sum)
template <class C, ENABLE_IF_T(not has_sum_v<C>)>
inline constexpr mem_value_type<C> sum(const C &v) {
    return std::accumulate(v.begin(), v.end(), mem_value_type<C>{});
}
template <typename T>
inline constexpr T sum(const std::initializer_list<T> &v) {
    return std::accumulate(v.begin(), v.end(), T{});
}

METHOD_EXPAND(product)
template <class C, ENABLE_IF_T(not has_product_v<C>)>
inline constexpr mem_value_type<C> product(const C &v) {
    return std::accumulate(v.begin(), v.end(), mem_value_type<C>{1}, std::multiplies<mem_value_type<C>>());
}
template <typename T>
inline constexpr T product(const std::initializer_list<T> &v) {
    return std::accumulate(v.begin(), v.end(), T{1}, std::multiplies<T>());
}

METHOD_EXPAND(product_xor)
template <class C, ENABLE_IF_T(not has_product_xor_v<C>)>
inline constexpr mem_value_type<C> product_xor(const C &v) {
    return std::accumulate(v.begin(), v.end(), mem_value_type<C>{0}, std::bit_xor<mem_value_type<C>>());
}
template <typename T>
inline constexpr T product_xor(const std::initializer_list<T> &v) {
    return std::accumulate(v.begin(), v.end(), T{0}, std::bit_xor<T>());
}

template <class C>
inline constexpr mem_value_type<C> maximum_subarray(const C &v) {
    assert(not v.empty());
    auto itr = v.begin();
    mem_value_type<C> tmp = *itr++;
    mem_value_type<C> res = tmp;
    while (itr != v.end()) {
        tmp += *itr;
        if (tmp < *itr) tmp = *itr;
        if (res < tmp) res = tmp;
        ++itr;
    }
    return res;
}
template <class C>
inline constexpr mem_value_type<C> maximum_subarray(const C &v, mem_value_type<C> init) {
    mem_value_type<C> res = init, tmp = init;
    for (const auto &a : v) {
        tmp += a;
        if (tmp < init) tmp = init;
        if (res < tmp) res = tmp;
    }
    return res;
}

METHOD_AND_FUNC_ARG_EXPAND(count)
METHOD_AND_FUNC_ARG_EXPAND(find)
METHOD_AND_FUNC_ARG_EXPAND(lower_bound)
METHOD_AND_FUNC_ARG_EXPAND(upper_bound)

template <class C, typename T>
inline constexpr bool contains(const C &c, const T &t) {
    return find(c, t) != c.end();
}

template <class C>
inline constexpr mem_value_type<C> gcd(const C &v) {
    mem_value_type<C> init(0);
    for (const auto &e : v) init = std::gcd(init, e);
    return init;
}

template <class C>
inline constexpr mem_value_type<C> average(const C &v) {
    assert(v.size());
    return sum(v) / v.size();
}

template <class C>
inline constexpr mem_value_type<C> median(const C &v) {
    assert(not v.empty());
    std::vector<size_t> u(v.size());
    std::iota(u.begin(), u.end(), 0);
    std::sort(u.begin(), u.end(), [&](size_t a, size_t b) {
        return v[a] < v[b];
    });
    if (v.size() & 1) {
        return v[u[v.size() / 2]];
    }
    // C++20
    // return std::midpoint(v[u[v.size() / 2]], v[u[v.size() / 2 - 1]]);
    return (v[u[v.size() / 2]] + v[u[v.size() / 2 - 1]]) / 2;
}

template <class C, typename U>
inline constexpr std::ptrdiff_t index(const C &v, const U &x) {
    return std::distance(v.begin(), find(v, x));
}

template <class C, ENABLE_IF_T(std::is_integral_v<mem_value_type<C>>)>
inline constexpr mem_value_type<C> mex(const C &v) {
    std::vector<bool> b(v.size() + 1);
    for (const auto &a : v) {
        if (0 <= a and a < b.size()) {
            b[a] = true;
        }
    }
    mem_value_type<C> ret;
    for (size_t i = 0; i < b.size(); i++) {
        if (not b[i]) {
            ret = i;
            break;
        }
    }
    return ret;
}

template <class C>
inline constexpr mem_difference_type<C> bisect_left(const C &v, const mem_value_type<C> &x) {
    return std::distance(v.begin(), lower_bound(v, x));
}
template <class C>
inline constexpr mem_difference_type<C> bisect_right(const C &v, const mem_value_type<C> &x) {
    return std::distance(v.begin(), upper_bound(v, x));
}
#line 6 "/home/shogo314/cpp_include/sh-library/base/functions.hpp"

template <typename T1, typename T2>
inline constexpr bool chmin(T1 &a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <typename T1, typename T2>
inline constexpr bool chmax(T1 &a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

inline constexpr long long max(const long long &t1, const long long &t2) {
    return std::max<long long>(t1, t2);
}

inline constexpr long long min(const long long &t1, const long long &t2) {
    return std::min<long long>(t1, t2);
}

using std::abs;
using std::gcd;
using std::lcm;
using std::size;

template <typename T>
constexpr T extgcd(const T &a, const T &b, T &x, T &y) {
    T d = a;
    if (b != 0) {
        d = extgcd(b, a % b, y, x);
        y -= (a / b) * x;
    } else {
        x = 1;
        y = 0;
    }
    return d;
}

template <typename M, typename N, class F, ENABLE_IF_T(std::is_integral_v<std::common_type_t<M, N>> and std::is_invocable_r_v<bool, F, std::common_type_t<M, N>>)>
inline constexpr std::common_type_t<M, N> binary_search(const M &ok, const N &ng, F f) {
    std::common_type_t<M, N> _ok = ok, _ng = ng;
    while (std::abs(_ok - _ng) > 1) {
        std::common_type_t<M, N> mid = (_ok + _ng) / 2;
        if (f(mid)) {
            _ok = mid;
        } else {
            _ng = mid;
        }
    }
    return _ok;
}

template <typename M, typename N, class F, ENABLE_IF_T(not std::is_integral_v<std::common_type_t<M, N>> and std::is_invocable_r_v<bool, F, std::common_type_t<M, N>>)>
inline constexpr std::common_type_t<M, N> binary_search(const M &ok, const N &ng, F f) {
    std::common_type_t<M, N> _ok = ok, _ng = ng;
    for (int i = 0; i < 100; i++) {
        std::common_type_t<M, N> mid = (_ok + _ng) / 2;
        if (f(mid)) {
            _ok = mid;
        } else {
            _ng = mid;
        }
    }
    return _ok;
}

/**
 * 0 <= x < a
 */
inline constexpr bool inrange(long long x, long long a) {
    return 0 <= x and x < a;
}
/**
 * a <= x < b
 */
inline constexpr bool inrange(long long x, long long a, long long b) {
    return a <= x and x < b;
}
/**
 * 0 <= x < a and 0 <= y < b
 */
inline constexpr bool inrect(long long x, long long y, long long a, long long b) {
    return 0 <= x and x < a and 0 <= y and y < b;
}
#line 8 "/home/shogo314/cpp_include/sh-library/base/io.hpp"

namespace tuple_io {
template <typename Tuple, size_t I, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& read_tuple(std::basic_istream<CharT, Traits>& is, Tuple& t) {
    is >> std::get<I>(t);
    if constexpr (I + 1 < std::tuple_size_v<Tuple>) {
        return read_tuple<Tuple, I + 1>(is, t);
    }
    return is;
}
template <typename Tuple, size_t I, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& write_tuple(std::basic_ostream<CharT, Traits>& os, const Tuple& t) {
    os << std::get<I>(t);
    if constexpr (I + 1 < std::tuple_size_v<Tuple>) {
        os << CharT(' ');
        return write_tuple<Tuple, I + 1>(os, t);
    }
    return os;
}
};  // namespace tuple_io

template <typename T1, typename T2, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::pair<T1, T2>& p) {
    is >> p.first >> p.second;
    return is;
}
template <typename... Types, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::tuple<Types...>& p) {
    return tuple_io::read_tuple<std::tuple<Types...>, 0>(is, p);
}
template <typename T, size_t N, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::array<T, N>& a) {
    for (auto& e : a) is >> e;
    return is;
}
template <typename T, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::vector<T>& v) {
    for (auto& e : v) is >> e;
    return is;
}

template <typename T1, typename T2, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::pair<T1, T2>& p) {
    os << p.first << CharT(' ') << p.second;
    return os;
}
template <typename... Types, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::tuple<Types...>& p) {
    return tuple_io::write_tuple<std::tuple<Types...>, 0>(os, p);
}
template <typename T, size_t N, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::array<T, N>& a) {
    for (size_t i = 0; i < N; ++i) {
        if (i) os << CharT(' ');
        os << a[i];
    }
    return os;
}
template <typename T, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::vector<T>& v) {
    for (size_t i = 0; i < v.size(); ++i) {
        if (i) os << CharT(' ');
        os << v[i];
    }
    return os;
}
template <typename T, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::set<T>& s) {
    for (auto itr = s.begin(); itr != s.end(); ++itr) {
        if (itr != s.begin()) os << CharT(' ');
        os << *itr;
    }
    return os;
}

/**
 * @brief 空行出力
 */
void print() { std::cout << '\n'; }
/**
 * @brief 出力して改行
 *
 * @tparam T 型
 * @param x 出力する値
 */
template <typename T>
void print(const T& x) { std::cout << x << '\n'; }
/**
 * @brief 空白区切りで出力して改行
 *
 * @tparam T 1つ目の要素の型
 * @tparam Tail 2つ目以降の要素の型
 * @param x 1つ目の要素
 * @param tail 2つ目以降の要素
 */
template <typename T, typename... Tail>
void print(const T& x, const Tail&... tail) {
    std::cout << x << ' ';
    print(tail...);
}

/**
 * @brief 空行出力
 */
void err() { std::cerr << std::endl; }
/**
 * @brief 出力して改行
 *
 * @tparam T 型
 * @param x 出力する値
 */
template <typename T>
void err(const T& x) { std::cerr << x << std::endl; }
/**
 * @brief 空白区切りで出力して改行
 *
 * @tparam T 1つ目の要素の型
 * @tparam Tail 2つ目以降の要素の型
 * @param x 1つ目の要素
 * @param tail 2つ目以降の要素
 */
template <typename T, typename... Tail>
void err(const T& x, const Tail&... tail) {
    std::cerr << x << ' ';
    err(tail...);
}
#line 3 "/home/shogo314/cpp_include/sh-library/base/type_alias.hpp"

using ll = long long;
using ull = unsigned long long;
using ld = long double;

template <typename T>
using vec = std::vector<T>;
template <typename T, int N>
using ary = std::array<T, N>;
using str = std::string;
using std::deque;
using std::list;
using std::map;
using std::multimap;
using std::multiset;
using std::pair;
using std::set;

using pl = pair<ll, ll>;
using pd = pair<ld, ld>;

template <typename T>
using vv = vec<vec<T>>;
template <typename T>
using vvv = vec<vec<vec<T>>>;
using vl = vec<ll>;
using vvl = vv<ll>;
using vvvl = vvv<ll>;
using vs = vec<str>;
using vc = vec<char>;
using vi = vec<int>;
using vb = vec<bool>;

template <typename T1, typename T2>
using vp = vec<pair<T1, T2>>;
using vpl = vec<pl>;
using vvpl = vv<pl>;
using vd = vec<ld>;
using vpd = vec<pd>;

template <int N>
using al = ary<ll, N>;
template <int N1, int N2>
using aal = ary<ary<ll, N2>, N1>;
template <int N>
using val = vec<al<N>>;
template <int N>
using avl = ary<vl,N>;

template <typename T>
using ml = std::map<ll, T>;
using mll = std::map<ll, ll>;
using sl = std::set<ll>;
using spl = set<pl>;
template <int N>
using sal = set<al<N>>;
template <int N>
using asl = ary<sl,N>;

template <typename T>
using heap_max = std::priority_queue<T, std::vector<T>, std::less<T>>;
template <typename T>
using heap_min = std::priority_queue<T, std::vector<T>, std::greater<T>>;
#line 3 "/home/shogo314/cpp_include/sh-library/base/macro.hpp"

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#define all(obj) (obj).begin(), (obj).end()

#define CONCAT_IMPL(x, y) __CONCAT(x, y)
#define UNIQUE_ID(base) CONCAT_IMPL(base, __COUNTER__)

#define GET_MACRO(_1, _2, _3, _4, NAME, ...) NAME

#define rep4(i, a, n, t) for (long long i = static_cast<long long>(a), i##_loop_end = static_cast<long long>(n), i##_loop_step = static_cast<long long>(t); i < i##_loop_end; i += i##_loop_step)
#define rep3(i, a, n) for (long long i = static_cast<long long>(a), i##_loop_end = static_cast<long long>(n); i < i##_loop_end; ++i)
#define rep2(i, n) rep3(i, 0, n)
#define rep1(n) rep2(UNIQUE_ID(loop_counter_), n)
#define rep(...) GET_MACRO(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define repd4(i, a, n, t) for (long long i = static_cast<long long>(n) - 1, i##_loop_end = static_cast<long long>(a), i##_loop_step = static_cast<long long>(t); i >= i##_loop_end; i -= i##_loop_step)
#define repd3(i, a, n) for (long long i = static_cast<long long>(n) - 1, i##_loop_end = static_cast<long long>(a); i >= i##_loop_end; --i)
#define repd2(i, n) repd3(i, 0, n)
#define repd(...) GET_MACRO(__VA_ARGS__, repd4, repd3, repd2)(__VA_ARGS__)

#define rrep(i, n) rep(i, 1, (n) + 1)
#define rrepd(i, n) repd(i, 1, (n) + 1)

inline void scan(){}
template<class Head,class... Tail>
inline void scan(Head&head,Tail&... tail){std::cin>>head;scan(tail...);}
#define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__)
#define STR(...) str __VA_ARGS__;scan(__VA_ARGS__)
#define IN(a, x) a x; std::cin >> x;
#define CHAR(x) char x; std::cin >> x;
#define VL(a,n) vl a(n); std::cin >> a;
#define AL(a,k) al<k> a; std::cin >> a;
#define AAL(a,n,m) aal<n,m> a; std::cin >> a;
#define VC(a,n) vc a(n); std::cin >> a;
#define VS(a,n) vs a(n); std::cin >> a;
#define VPL(a,n) vpl a(n); std::cin >> a;
#define VAL(a,n,k) val<k> a(n); std::cin >> a;
#define VVL(a,n,m) vvl a(n,vl(m)); std::cin >> a;
#define SL(a,n) sl a;{VL(b,n);a=sl(all(b));}

#define NO std::cout << "NO" << std::endl; return;
#define YES std::cout << "YES" << std::endl; return;
#define No std::cout << "No" << std::endl; return;
#define Yes std::cout << "Yes" << std::endl; return;
#define Takahashi std::cout << "Takahashi" << std::endl; return;
#define Aoki std::cout << "Aoki" << std::endl; return;
#line 7 "/home/shogo314/cpp_include/sh-library/base/vector_func.hpp"

#line 9 "/home/shogo314/cpp_include/sh-library/base/vector_func.hpp"

template <typename T>
std::vector<std::ptrdiff_t> sorted_idx(const std::vector<T> &v, bool reverse = false) {
    std::vector<std::ptrdiff_t> ret(v.size());
    std::iota(ret.begin(), ret.end(), 0);
    std::sort(ret.begin(), ret.end(), [&](std::ptrdiff_t i, std::ptrdiff_t j) {
        return v[i] < v[j];
    });
    if (reverse) std::reverse(ret.begin(), ret.end());
    return ret;
}

template <typename T>
inline std::vector<T> &operator++(std::vector<T> &v) {
    for (auto &e : v) e++;
    return v;
}
template <typename T>
inline std::vector<T> operator++(std::vector<T> &v, int) {
    auto res = v;
    for (auto &e : v) e++;
    return res;
}
template <typename T>
inline std::vector<T> &operator--(std::vector<T> &v) {
    for (auto &e : v) e--;
    return v;
}
template <typename T>
inline std::vector<T> operator--(std::vector<T> &v, int) {
    auto res = v;
    for (auto &e : v) e--;
    return res;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator+=(std::vector<T> &v1, const std::vector<U> &v2) {
    if (v2.size() > v1.size()) {
        v1.resize(v2.size());
    }
    for (size_t i = 0; i < v2.size(); i++) {
        v1[i] += v2[i];
    }
    return v1;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator+(const std::vector<T> &v1, const std::vector<U> &v2) {
    std::vector<T> res(v1);
    return res += v2;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator+=(std::vector<T> &v, const U &u) {
    for (T &e : v) {
        e += u;
    }
    return v;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator+(const std::vector<T> &v, const U &u) {
    std::vector<T> res(v);
    return res += u;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator+(const U &u, const std::vector<T> &v) {
    std::vector<T> res(v);
    return res += u;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator*=(std::vector<T> &v1, const std::vector<U> &v2) {
    if (v2.size() > v1.size()) {
        v1.resize(v2.size());
    }
    for (size_t i = 0; i < v2.size(); i++) {
        v1[i] *= v2[i];
    }
    for (size_t i = v2.size(); i < v1.size(); i++) {
        v1[i] *= U(0);
    }
    return v1;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator*(const std::vector<T> &v1, const std::vector<U> &v2) {
    std::vector<T> res(v1);
    return res *= v2;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator*=(std::vector<T> &v, const U &u) {
    for (T &e : v) {
        e *= u;
    }
    return v;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator*(const std::vector<T> &v, const U &u) {
    std::vector<T> res(v);
    return res *= u;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator*(const U &u, const std::vector<T> &v) {
    std::vector<T> res(v);
    return res *= u;
}

template <typename T, typename U>
inline std::vector<T> &assign(std::vector<T> &v1, const std::vector<U> &v2) {
    v1.assign(v2.begin(), v2.end());
    return v1;
}

template <typename T, typename U>
inline std::vector<T> &extend(std::vector<T> &v1, const std::vector<U> &v2) {
    v1.insert(v1.end(), v2.begin(), v2.end());
    return v1;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator|=(std::vector<T> &v1, const std::vector<U> &v2) {
    return extend(v1, v2);
}

template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>
inline std::vector<T> &operator|=(std::vector<T> &v, const U &u) {
    std::vector<T> w(v);
    v.clear();
    for (int i = 0; i < u; i++) {
        extend(v, w);
    }
    return v;
}

template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>
inline std::vector<T> operator|(const std::vector<T> &v, const U &u) {
    std::vector<T> res(v);
    return res |= u;
}

template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>
inline std::vector<T> operator|(const U &u, const std::vector<T> &v) {
    std::vector<T> res(v);
    return res |= u;
}

template <typename T>
inline std::vector<T> abs(const std::vector<T> &v) {
    std::vector<T> ret;
    ret.reserve(v.size());
    for (const T &e : v) ret.push_back(std::abs(e));
    return ret;
}

template <typename T>
std::vector<T> cumulative_sum(std::vector<T> v) {
    v.insert(v.begin(), T{});
    std::vector<T> ret(v.size());
    std::partial_sum(v.begin(), v.end(), ret.begin());
    return ret;
}

template <typename T, ENABLE_IF_T(std::is_integral_v<T>)>
std::vector<T> iota(T n) {
    assert(n >= 0);
    std::vector<T> ret(n);
    std::iota(ret.begin(), ret.end(), 0);
    return ret;
}

template <typename T>
std::vector<T> unique(const std::vector<T> &v) {
    std::vector<T> res(v);
    std::sort(res.begin(), res.end());
    res.erase(std::unique(res.begin(), res.end()), res.end());
    return res;
}

long long radix_convert(const std::vector<long long> &v, int base = 10) {
    long long res = 0;
    for (int i = v.size() - 1; i >= 0; i--) {
        res <<= base;
        res += v[i];
    }
    return res;
}

std::vector<long long> radix_convert(long long v, int base = 10) {
    std::vector<long long> res;
    while (v > 0) {
        res.push_back(v % base);
        v /= base;
    }
    std::reverse(res.begin(), res.end());
    return res;
}
#line 5 "/home/shogo314/cpp_include/sh-library/base/bit.hpp"

/**
 * @brief 2進数の文字列をlong longにする
 */
long long btoll(std::string s, char one = '1') {
    long long res = 0;
    for (char c : s) {
        res <<= 1;
        if (c == one) ++res;
    }
    return res;
}

#if __cplusplus < 202000L

/**
 * @brief 立っているビットを数える
 * __builtin_popcountll
 */
int popcount(long long a) {
    assert(a >= 0);
    return __builtin_popcountll((unsigned long long)a);
}
/**
 * @brief 左から連続した0のビットを数える
 * __builtin_clzll
 */
int countl_zero(long long a) {
    assert(a >= 0);
    return __builtin_clzll((unsigned long long)a);
}
/**
 * @brief 右から連続した0のビットを数える
 * __builtin_ctzll
 */
int countr_zero(long long a) {
    assert(a >= 0);
    return __builtin_ctzll((unsigned long long)a);
}

#else

#include <bit>
#define BIT_FUNC_EXPAND(func)                      \
    inline constexpr long long func(long long a) { \
        assert(a >= 0);                            \
        return std::func((unsigned long long)a);   \
    }

/**
 * @brief 立っているビットを数える
 */
BIT_FUNC_EXPAND(popcount)
/**
 * @brief 左から連続した0のビットを数える
 */
BIT_FUNC_EXPAND(countl_zero)
/**
 * @brief 左から連続した1のビットを数える
 */
BIT_FUNC_EXPAND(countl_one)
/**
 * @brief 右から連続した0のビットを数える
 */
BIT_FUNC_EXPAND(countr_zero)
/**
 * @brief 右から連続した1のビットを数える
 */
BIT_FUNC_EXPAND(countr_one)
/**
 * @brief 整数値を2の累乗値に切り上げる
 */
BIT_FUNC_EXPAND(bit_ceil)
/**
 * @brief 整数値を2の累乗値に切り下げる
 */
BIT_FUNC_EXPAND(bit_floor)
/**
 * @brief 値を表現するために必要なビット幅を求める
 */
BIT_FUNC_EXPAND(bit_width)

#endif
#line 4 "main.cpp"
using mint = modint998244353;
using C = Combination<mint>;

void solve() {
    map<al<2>, mint> mm;
    auto f = [&](ll k, ll t) -> mint {
        if (mm.contains({k, t})) {
            return mm[{k, t}];
        }
        mint tmp = 0;
        rep(p, k + 1) {
            tmp += mint(t + p).inv() * C::C(k, p);
        }
        mm[{k, t}] = tmp;
        return tmp;
    };
    LL(N);
    VL(A, 2 * N);
    ll m = max(A);
    al<6> cnt = {};
    rep(i, N) {
        if (A[2 * i] == m || A[2 * i + 1] == m) {
            if (A[2 * i] == m && A[2 * i + 1] == m) {
                cnt[5]++;
            } else if (A[2 * i] == m - 1 || A[2 * i + 1] == m - 1) {
                cnt[4]++;
            } else {
                cnt[3]++;
            }
        } else {
            if (A[2 * i] == m - 1 && A[2 * i + 1] == m - 1) {
                cnt[2]++;
            } else if (A[2 * i] == m - 1 || A[2 * i + 1] == m - 1) {
                cnt[1]++;
            } else {
                cnt[0]++;
            }
        }
    }
    vec<mint> ans(2 * N);
    rep(i, 2 * N) {
        if (A[i] < m - 1) {
            continue;
        }
        if (A[i] == m) {
            mint tmp = 0;
            ll t = cnt[5];
            ll k = cnt[3] + cnt[4];
            if (A[i ^ 1] < m) {
                k--;
                t++;
            }
            mint b = mint(2).pow(1 + k).inv();
            assert(t > 0);
            tmp += b * f(k, t);
            if (cnt[5]) {
                ans[i] = tmp;
                continue;
            }
            t = cnt[2] + cnt[3] + cnt[4] * 2;
            k = cnt[1];
            b = mint(2).pow(cnt[3] + cnt[4] + k).inv();
            assert(t > 0);
            tmp += b * f(k, t);
            ans[i] = tmp;
        } else {
            if (cnt[5])
                continue;
            mint tmp = 0;
            ll t = cnt[2] + cnt[3] + cnt[4] * 2;
            ll k = cnt[1];
            if (A[i ^ 1] < m - 1) {
                t++;
                k--;
            }
            mint b = mint(2).pow(cnt[3] + cnt[4] + k + (A[i ^ 1] <= m - 1)).inv();
            assert(t > 0);
            tmp += b * f(k, t);
            ans[i] = tmp;
        }
    }
    print(ans);
}

int main() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    solve();
}

Submission Info

Compile Error

/home/shogo314/cpp_include/ou-library/combinatorics.hpp: In member function 'int CombinationPQ::C(long long int, long long int)':
/home/shogo314/cpp_include/ou-library/combinatorics.hpp:217:42: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]

Judge Result