Submission #67786142

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Source Code Expand

// #undef YOSUPO_LOCAL

#if 0 and !defined(__clang__)
#include <vector>
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#pragma GCC optimize("Ofast")
#endif


#include <stdio.h>
#include <unistd.h>

#include <algorithm>
#include <array>
#include <bit>
#include <cassert>
#include <cctype>
#include <cstdint>
#include <cstdio>
#include <cstring>
#include <sstream>
#include <string>
#include <type_traits>
#include <vector>



namespace yosupo {

namespace internal {

template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value ||
                                  internal::is_signed_int128<T>::value ||
                                  internal::is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

template <class T>
using is_integral_t = std::enable_if_t<is_integral<T>::value>;

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace yosupo

namespace yosupo {

struct Scanner {
  public:
    Scanner(const Scanner&) = delete;
    Scanner& operator=(const Scanner&) = delete;

    Scanner(FILE* fp) : fd(fileno(fp)) { line[0] = 127; }

    void read() {}
    template <class H, class... T> void read(H& h, T&... t) {
        bool f = read_single(h);
        assert(f);
        read(t...);
    }

    int read_unsafe() { return 0; }
    template <class H, class... T> int read_unsafe(H& h, T&... t) {
        bool f = read_single(h);
        if (!f) return 0;
        return 1 + read_unsafe(t...);
    }

    int close() { return ::close(fd); }

  private:
    static constexpr int SIZE = 1 << 15;

    int fd = -1;
    std::array<char, SIZE + 1> line;
    int st = 0, ed = 0;
    bool eof = false;

    bool read_single(std::string& ref) {
        if (!skip_space()) return false;
        ref = "";
        while (true) {
            char c = top();
            if (c <= ' ') break;
            ref += c;
            st++;
        }
        return true;
    }
    bool read_single(double& ref) {
        std::string s;
        if (!read_single(s)) return false;
        ref = std::stod(s);
        return true;
    }

    template <class T,
              std::enable_if_t<std::is_same<T, char>::value>* = nullptr>
    bool read_single(T& ref) {
        if (!skip_space<50>()) return false;
        ref = top();
        st++;
        return true;
    }

    template <class T,
              internal::is_signed_int_t<T>* = nullptr,
              std::enable_if_t<!std::is_same<T, char>::value>* = nullptr>
    bool read_single(T& sref) {
        using U = internal::to_unsigned_t<T>;
        if (!skip_space<50>()) return false;
        bool neg = false;
        if (line[st] == '-') {
            neg = true;
            st++;
        }
        U ref = 0;
        do {
            ref = 10 * ref + (line[st++] & 0x0f);
        } while (line[st] >= '0');
        sref = neg ? -ref : ref;
        return true;
    }
    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<!std::is_same<U, char>::value>* = nullptr>
    bool read_single(U& ref) {
        if (!skip_space<50>()) return false;
        ref = 0;
        do {
            ref = 10 * ref + (line[st++] & 0x0f);
        } while (line[st] >= '0');
        return true;
    }

    bool reread() {
        if (ed - st >= 50) return true;
        if (st > SIZE / 2) {
            std::memmove(line.data(), line.data() + st, ed - st);
            ed -= st;
            st = 0;
        }
        if (eof) return false;
        auto u = ::read(fd, line.data() + ed, SIZE - ed);
        if (u == 0) {
            eof = true;
            line[ed] = '\0';
            u = 1;
        }
        ed += int(u);
        line[ed] = char(127);
        return true;
    }

    char top() {
        if (st == ed) {
            bool f = reread();
            assert(f);
        }
        return line[st];
    }

    template <int TOKEN_LEN = 0> bool skip_space() {
        while (true) {
            while (line[st] <= ' ') st++;
            if (ed - st > TOKEN_LEN) return true;
            if (st > ed) st = ed;
            for (auto i = st; i < ed; i++) {
                if (line[i] <= ' ') return true;
            }
            if (!reread()) return false;
        }
    }
};

struct Printer {
  public:
    template <char sep = ' ', bool F = false> void write() {}
    template <char sep = ' ', bool F = false, class H, class... T>
    void write(const H& h, const T&... t) {
        if (F) write_single(sep);
        write_single(h);
        write<true>(t...);
    }
    template <char sep = ' ', class... T> void writeln(const T&... t) {
        write<sep>(t...);
        write_single('\n');
    }

    Printer(FILE* _fp) : fd(fileno(_fp)) {}
    ~Printer() { flush(); }

    int close() {
        flush();
        return ::close(fd);
    }

    void flush() {
        if (pos) {
            auto res = ::write(fd, line.data(), pos);
            assert(res != -1);
            pos = 0;
        }
    }

  private:
    static std::array<std::array<char, 2>, 100> small;
    static std::array<unsigned long long, 20> tens;

    static constexpr size_t SIZE = 1 << 15;
    int fd;
    std::array<char, SIZE> line;
    size_t pos = 0;
    std::stringstream ss;

    template <class T,
              std::enable_if_t<std::is_same<char, T>::value>* = nullptr>
    void write_single(const T& val) {
        if (pos == SIZE) flush();
        line[pos++] = val;
    }

    template <class T,
              internal::is_signed_int_t<T>* = nullptr,
              std::enable_if_t<!std::is_same<char, T>::value>* = nullptr>
    void write_single(const T& val) {
        using U = internal::to_unsigned_t<T>;
        if (val == 0) {
            write_single('0');
            return;
        }
        if (pos > SIZE - 50) flush();
        U uval = val;
        if (val < 0) {
            write_single('-');
            uval = -uval;
        }
        write_unsigned(uval);
    }

    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<!std::is_same<char, U>::value>* = nullptr>
    void write_single(U uval) {
        if (uval == 0) {
            write_single('0');
            return;
        }
        if (pos > SIZE - 50) flush();

        write_unsigned(uval);
    }

    static int calc_len(uint64_t x) {
        int i = ((63 - std::countl_zero(x)) * 3 + 3) / 10;
        if (x < tens[i])
            return i;
        else
            return i + 1;
    }

    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<2 >= sizeof(U)>* = nullptr>
    void write_unsigned(U uval) {
        size_t len = calc_len(uval);
        pos += len;

        char* ptr = line.data() + pos;
        while (uval >= 100) {
            ptr -= 2;
            memcpy(ptr, small[uval % 100].data(), 2);
            uval /= 100;
        }
        if (uval >= 10) {
            memcpy(ptr - 2, small[uval].data(), 2);
        } else {
            *(ptr - 1) = char('0' + uval);
        }
    }

    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<4 == sizeof(U)>* = nullptr>
    void write_unsigned(U uval) {
        std::array<char, 8> buf;
        memcpy(buf.data() + 6, small[uval % 100].data(), 2);
        memcpy(buf.data() + 4, small[uval / 100 % 100].data(), 2);
        memcpy(buf.data() + 2, small[uval / 10000 % 100].data(), 2);
        memcpy(buf.data() + 0, small[uval / 1000000 % 100].data(), 2);

        if (uval >= 100000000) {
            if (uval >= 1000000000) {
                memcpy(line.data() + pos, small[uval / 100000000 % 100].data(),
                       2);
                pos += 2;
            } else {
                line[pos] = char('0' + uval / 100000000);
                pos++;
            }
            memcpy(line.data() + pos, buf.data(), 8);
            pos += 8;
        } else {
            size_t len = calc_len(uval);
            memcpy(line.data() + pos, buf.data() + (8 - len), len);
            pos += len;
        }
    }

    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<8 == sizeof(U)>* = nullptr>
    void write_unsigned(U uval) {
        size_t len = calc_len(uval);
        pos += len;

        char* ptr = line.data() + pos;
        while (uval >= 100) {
            ptr -= 2;
            memcpy(ptr, small[uval % 100].data(), 2);
            uval /= 100;
        }
        if (uval >= 10) {
            memcpy(ptr - 2, small[uval].data(), 2);
        } else {
            *(ptr - 1) = char('0' + uval);
        }
    }

    template <
        class U,
        std::enable_if_t<internal::is_unsigned_int128<U>::value>* = nullptr>
    void write_unsigned(U uval) {
        static std::array<char, 50> buf;
        size_t len = 0;
        while (uval > 0) {
            buf[len++] = char((uval % 10) + '0');
            uval /= 10;
        }
        std::reverse(buf.begin(), buf.begin() + len);
        memcpy(line.data() + pos, buf.data(), len);
        pos += len;
    }

    void write_single(const std::string& s) {
        for (char c : s) write_single(c);
    }
    void write_single(const char* s) {
        size_t len = strlen(s);
        for (size_t i = 0; i < len; i++) write_single(s[i]);
    }
    template <class T> void write_single(const std::vector<T>& val) {
        auto n = val.size();
        for (size_t i = 0; i < n; i++) {
            if (i) write_single(' ');
            write_single(val[i]);
        }
    }
};

inline std::array<std::array<char, 2>, 100> Printer::small = [] {
    std::array<std::array<char, 2>, 100> table;
    for (int i = 0; i <= 99; i++) {
        table[i][1] = char('0' + (i % 10));
        table[i][0] = char('0' + (i / 10 % 10));
    }
    return table;
}();
inline std::array<unsigned long long, 20> Printer::tens = [] {
    std::array<unsigned long long, 20> table;
    for (int i = 0; i < 20; i++) {
        table[i] = 1;
        for (int j = 0; j < i; j++) {
            table[i] *= 10;
        }
    }
    return table;
}();

}  // namespace yosupo

#include <concepts>
#include <cstdlib>


#include <cmath>



namespace yosupo {

using i8 = int8_t;
using u8 = uint8_t;
using i16 = int16_t;
using u16 = uint16_t;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;

using f32 = float;
using f64 = double;

}  // namespace yosupo

namespace yosupo {
// x * inv_u32(x) = 1 (mod 2^32)
inline constexpr u32 inv_u32(const u32 x) {
    u32 inv = 1;
    for (int i = 0; i < 5; i++) {
        inv *= 2u - inv * x;
    }
    return inv;
}

inline constexpr u64 pow_mod_u64(u64 x, u64 n, u64 m) {
    if (m == 1) return 0;
    u64 r = 1;
    u64 y = x % m;
    while (n) {
        if (n & 1) r = (u64)((u128)(1) * r * y % m);
        y = (u64)((u128)(1) * y * y % m);
        n >>= 1;
    }
    return r;
}

inline u64 isqrt(u64 a) {
    if (a == u64(-1)) return (u64(1) << 32) - 1;
    u64 x = (u64)std::sqrt((double)a);
    return x * x > a ? x - 1 : x;
}

// integer k-th root: floor(a^(1/k))
inline u64 iroot(u64 a, int k) {
    if (k == 2) return isqrt(a);
    if (k == 1 || a == 0) return a;
    if (k >= 64 || a < (u64(1) << k)) return 1;

    // is (b^k <= a)?
    auto check = [&](u64 b) {
        u128 result = 1;
        for (int i = 0; i < k; i++) {
            result *= b;
            if (result > a) return false;
        }
        return true;
    };

    // lw^k <= a < up^k
    u64 lw = 2;
    u64 up = 1LL << ((64 + k - 1) / k);
    while (up - lw > 1) {
        u64 mid = (lw + up) / 2;
        if (check(mid)) {
            lw = mid;
        } else {
            up = mid;
        }
    }

    return lw;
}

}  // namespace yosupo

#include <initializer_list>
#include <limits>


namespace yosupo {

inline constexpr bool is_prime(u32 n) {
    if (n == 2) return true;
    if (n % 2 == 0) return false;
    u64 d = n - 1;
    while (d % 2 == 0) d /= 2;
    for (u64 a : {2, 7, 61}) {
        if (a % n == 0) return true;
        u64 t = d;
        u64 y = pow_mod_u64(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = (u64)((u128)(1) * y * y % n);
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
inline constexpr bool is_prime(u64 n) {
    if (n <= std::numeric_limits<u32>::max()) {
        return is_prime((u32)n);
    }
    if (n % 2 == 0) return false;
    u64 d = n - 1;
    while (d % 2 == 0) d /= 2;
    for (u64 a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
        if (a % n == 0) return true;
        u64 t = d;
        u64 y = pow_mod_u64(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = (u64)((u128)(1) * y * y % n);
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
inline bool is_prime(i32 n) {
    if (n <= 1) return false;
    return is_prime((u32)n);
}
inline bool is_prime(i64 n) {
    if (n <= 1) return false;
    return is_prime((u64)n);
}

// lpf_table[i] = the smallest prime factor of i
inline std::vector<i32> lpf_table(i32 n) {
    std::vector<i32> table(n + 1, -1);
    std::vector<int> primes;
    for (int d = 2; d <= n; d++) {
        if (table[d] == -1) {
            primes.push_back(d);
            table[d] = d;
        }
        for (int p : primes) {
            if (p * d > n || p > table[d]) break;
            table[p * d] = p;
        }
    }
    return table;
}

// enumerate primes no more than n
inline std::vector<i32> primes(i32 n) {
    std::vector<i32> table = lpf_table(n);
    std::vector<i32> p;
    for (int i = 2; i <= n; i++) {
        if (table[i] == i) p.push_back(i);
    }
    return p;
}

}  // namespace yosupo

namespace yosupo {

template <i32 MOD>
    requires requires {
        MOD % 2 == 1 && 1 <= MOD&& MOD <= (1 << 30) - 1;
        is_prime(MOD);
    }
struct ModInt {
    static constexpr i32 mod() { return MOD; }

    constexpr ModInt() : x(0) {}

    // It's OK because _x * B2 < 2**32 * MOD
    constexpr ModInt(u32 _x) : x(reduce_mul(_x, B2)) {}

    constexpr ModInt(std::signed_integral auto _x)
        : ModInt((u32)(_x % MOD + MOD)) {}
    constexpr ModInt(std::unsigned_integral auto _x)
        : ModInt((u32)(_x % MOD)) {}

    constexpr i32 val() const {
        u32 y = reduce_mul(x, 1);
        return y < MOD ? y : y - MOD;
    }

    constexpr ModInt operator+() const { return *this; }
    constexpr ModInt operator-() const { return ModInt() -= *this; }

    constexpr ModInt& operator+=(const ModInt& rhs) {
        x += rhs.x;
        x = std::min(x, x - 2 * MOD);
        return *this;
    }
    constexpr friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) += rhs;
    }

    constexpr ModInt& operator-=(const ModInt& rhs) {
        x += 2 * MOD - rhs.x;
        x = std::min(x, x - 2 * MOD);
        return *this;
    }
    constexpr friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) -= rhs;
    }

    constexpr ModInt& operator*=(const ModInt& rhs) {
        x = reduce_mul(x, rhs.x);
        return *this;
    }
    constexpr friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) *= rhs;
    }

    constexpr ModInt& operator/=(const ModInt& rhs) {
        return *this *= rhs.inv();
    }
    constexpr friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) /= rhs;
    }

    friend bool operator==(const ModInt& lhs, const ModInt& rhs) {
        return std::min(lhs.x, lhs.x - MOD) == std::min(rhs.x, rhs.x - MOD);
    }

    constexpr ModInt pow(u64 n) const {
        ModInt v = *this, r = 1;
        while (n) {
            if (n & 1) r *= v;
            v *= v;
            n >>= 1;
        }
        return r;
    }
    constexpr ModInt inv() const { return pow(MOD - 2); }

    std::string dump() const { return std::to_string(val()); }

  private:
    u32 x;  // [0, 2 * MOD)

    static constexpr u32 B = ((u64(1) << 32)) % MOD;
    static constexpr u32 B2 = u64(1) * B * B % MOD;
    static constexpr u32 INV = -inv_u32(MOD);

    // Input: (l * r) must be no more than (2^32 * MOD)
    // Output: ((l * r) / 2^32) % MOD
    static constexpr u32 reduce_mul(u32 l, u32 r) {
        u64 x = u64(1) * l * r;
        x += u64(u32(x) * INV) * MOD;
        return u32(x >> 32);
    }
};

using ModInt998244353 = ModInt<998244353>;
using ModInt1000000007 = ModInt<1000000007>;

}  // namespace yosupo


namespace yosupo {

namespace internal {

template <class T> struct CombState {
    int size = 1;
    std::vector<T> fact = {T(1)};
    std::vector<T> inv_fact = {T(1)};
    std::vector<T> inv = {T(0)};

    void extend() {
        fact.resize(2 * size);
        inv_fact.resize(2 * size);
        inv.resize(2 * size);
        for (int i = size; i < 2 * size; i++) {
            fact[i] = fact[i - 1] * T(i);
        }
        inv_fact[2 * size - 1] = fact[2 * size - 1].inv();
        for (int i = 2 * size - 1; i >= size + 1; i--) {
            inv_fact[i - 1] = inv_fact[i] * T(i);
        }

        for (int i = size; i < 2 * size; i++) {
            inv[i] = inv_fact[i] * fact[i - 1];
        }

        size *= 2;
    }
};

template <class T> CombState<T>& get_comb_state(int n) {
    static CombState<T> state;
    while (state.size <= n) state.extend();
    return state;
}

}  // namespace internal

template <class T> T fact(int x) {
    assert(0 <= x);
    return internal::get_comb_state<T>(x).fact[x];
}

template <class T> T inv_fact(int x) {
    assert(0 <= x);
    return internal::get_comb_state<T>(x).inv_fact[x];
}

template <class T> T inv(int x) {
    assert(0 <= x);
    return internal::get_comb_state<T>(x).inv[x];
}

namespace internal {
template <class T> T comb(int n, int k) {
    return fact<T>(n) * inv_fact<T>(k) * inv_fact<T>(n - k);
}
}  // namespace internal

template <class T> T comb(int n, int k) {
    assert(0 <= k);
    if (0 <= n && n < k) return 0;

    if (n >= 0) {
        return internal::comb<T>(n, k);
    }
    T x = internal::comb<T>(k - n - 1, k);
    if (k % 2) x = -x;
    return x;
}

}  // namespace yosupo

#include <numeric>
#include <utility>



namespace yosupo {
using std::countr_zero;

inline int countr_zero(unsigned __int128 x) {
    auto lo = (unsigned long long)(x);
    auto hi = (unsigned long long)(x >> 64);
    return lo ? std::countr_zero(lo) : 64 + std::countr_zero(hi);
}

template <class T>
    requires requires(T x) {
        { x.countr_zero() } -> std::same_as<int>;
    }
int countr_zero(T x) {
    return x.countr_zero();
}

}  // namespace yosupo

namespace yosupo {

// sign
template <class T>
    requires std::is_integral_v<T>
int sgn(T x) {
    if (x == 0) return 0;
    return x > 0 ? 1 : -1;
}
inline int sgn(__int128 x) {
    if (x == 0) return 0;
    return x > 0 ? 1 : -1;
}
// for custom class
template <class T>
    requires requires(T x) {
        { x.sgn() } -> std::same_as<int>;
    }
int sgn(T x) {
    return x.sgn();
}

// abs
template <std::integral T> inline T abs(T x) { return std::abs(x); }
inline i128 abs(i128 x) { return x < 0 ? -x : x; }
template <class T>
    requires requires(T x) {
        { x.abs() } -> std::same_as<T>;
    }
T abs(T x) {
    return x.abs();
}

// gcd
using std::gcd;
inline u128 gcd(u128 a, u128 b) {
    if (a == 0) return b;
    if (b == 0) return a;
    int shift;
    {
        int a_bsf = countr_zero(a);
        a >>= a_bsf;
        int b_bsf = countr_zero(b);
        b >>= b_bsf;
        shift = std::min(a_bsf, b_bsf);
    }
    while (a != b) {
        if (a > b) std::swap(a, b);
        b -= a;
        b >>= countr_zero(b);
    }
    return (a << shift);
}
inline i128 gcd(i128 a, i128 b) { return gcd((u128)abs(a), (u128)abs(b)); }
template <class T>
    requires requires(T x) {
        { T::gcd(x, x) } -> std::same_as<T>;
    }
T gcd(T x, T y) {
    return T::gcd(x, y);
}

}  // namespace yosupo


#include <bitset>
#include <iostream>
#include <map>
#include <queue>
#include <ranges>
#include <set>


#include <cstddef>
#include <tuple>


namespace yosupo {

inline std::string dump(const std::string& t) { return t; }
inline std::string dump(const char* t) { return t; }

template <std::integral T> std::string dump(T t) { return std::to_string(t); }

inline std::string dump(const u128& t) {
    if (t == 0) {
        return "0";
    }

    std::string s;
    u128 x = t;
    while (x) {
        s += char(x % 10 + '0');
        x /= 10;
    }
    std::ranges::reverse(s);
    return s;
}

inline std::string dump(const i128& t) {
    if (t < 0) {
        return "-" + dump((u128)(-t));
    } else {
        return dump((u128)(t));
    }
}

template <std::floating_point T> std::string dump(T t) {
    return std::to_string(t);
}

template <class T>
    requires requires(T t) { t.dump(); }
std::string dump(T t);
template <class T>
    requires(!requires(T t) { t.dump(); }) && (requires(T t) { t.val(); })
std::string dump(T t);

template <class T, std::size_t N> std::string dump(const std::array<T, N>&);
template <class T> std::string dump(const std::vector<T>&);
template <class T1, class T2> std::string dump(const std::pair<T1, T2>&);
template <class K, class V> std::string dump(const std::map<K, V>&);
template <class T> std::string dump(const std::set<T>&);
template <class... Ts> std::string dump(const std::tuple<Ts...>& t);

template <class T>
    requires requires(T t) { t.dump(); }
std::string dump(T t) {
    return dump(t.dump());
}

template <class T>
    requires(!requires(T t) { t.dump(); }) && (requires(T t) { t.val(); })
std::string dump(T t) {
    return dump(t.val());
}

template <class T, std::size_t N> std::string dump(const std::array<T, N>& a) {
    std::string s = "[";
    for (size_t i = 0; i < N; i++) {
        if (i) {
            s += ", ";
        }
        s += dump(a[i]);
    }
    s += "]";
    return s;
}

template <class T> std::string dump(const std::vector<T>& v) {
    std::string s = "[";
    for (std::size_t i = 0; i < v.size(); ++i) {
        s += dump(v[i]);
        if (i + 1 != v.size()) {
            s += ", ";
        }
    }
    s += "]";
    return s;
}

template <class T1, class T2> std::string dump(const std::pair<T1, T2>& p) {
    std::string s = "(";
    s += dump(p.first);
    s += ", ";
    s += dump(p.second);
    s += ")";
    return s;
}

template <class K, class V> std::string dump(const std::map<K, V>& m) {
    std::string s = "{";
    for (auto it = m.begin(); it != m.end(); ++it) {
        if (it != m.begin()) {
            s += ", ";
        }
        s += dump(it->first);
        s += ": ";
        s += dump(it->second);
    }
    s += "}";
    return s;
}

template <class T> std::string dump(const std::set<T>& s) {
    std::string str = "{";
    for (auto it = s.begin(); it != s.end(); ++it) {
        if (it != s.begin()) {
            str += ", ";
        }
        str += dump(*it);
    }
    str += "}";
    return str;
}

template <class... Ts> std::string dump(const std::tuple<Ts...>& t) {
    std::string s = "(";
    [&]<std::size_t... I>(std::index_sequence<I...>) {
        ((s += dump(std::get<I>(t)) + ((I < sizeof...(Ts) - 1) ? ", " : "")),
         ...);
    }(std::make_index_sequence<sizeof...(Ts)>());
    s += ")";
    return s;
}

}  // namespace yosupo

#include <functional>
#include <span>

namespace yosupo {

template <class T> bool chmin(T& a, const T& b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> bool chmax(T& a, const T& b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> T floor_div(T x, T y) {
    auto d = x / y;
    auto r = x % y;
    if (r == 0) return d;
    if ((r > 0) == (y > 0)) return d;
    return d - 1;
}
template <class T> T ceil_div(T x, T y) {
    auto d = x / y;
    auto r = x % y;
    if (r == 0) return d;
    if ((r > 0) == (y > 0)) return d + 1;
    return d;
}

template <std::ranges::input_range R>
std::vector<std::ranges::range_value_t<R>> to_vec(R&& r) {
    auto common = r | std::views::common;
    return std::vector(common.begin(), common.end());
}

template <class T, class Comp = std::equal_to<>>
void dedup(std::vector<T>& v, Comp comp = Comp{}) {
    auto it = std::ranges::unique(v, comp);
    v.erase(it.begin(), it.end());
}

template <size_t N, class T> std::span<T, N> subspan(std::span<T> a, int idx) {
    return a.subspan(idx).template first<N>();
}

inline auto rep(int l, int r) {
    if (l > r) return std::views::iota(l, l);
    return std::views::iota(l, r);
}

}  // namespace yosupo
using namespace yosupo;

using std::abs, std::pow, std::sqrt;
using std::array, std::vector, std::string, std::queue, std::deque;
using std::countl_zero, std::countl_one, std::countr_zero, std::countr_one;
using std::istream, std::ostream, std::cerr, std::endl;
using std::min, std::max, std::swap;
using std::pair, std::tuple, std::bitset;
using std::popcount;
using std::priority_queue, std::set, std::multiset, std::map;
using std::views::iota, std::views::reverse;

namespace ranges = std::ranges;
using ranges::sort, ranges::copy_n;

using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;

#ifdef YOSUPO_LOCAL

struct PrettyOS {
    ostream& os;
    bool first;

    template <class T> auto operator<<(T&& x) {
        if (!first) os << ", ";
        first = false;
        os << yosupo::dump(x);
        return *this;
    }
};
template <class... T> void dbg0(T&&... t) {
    (PrettyOS{cerr, true} << ... << t);
}
#define dbg(...)                                            \
    do {                                                    \
        cerr << __LINE__ << " : " << #__VA_ARGS__ << " = "; \
        dbg0(__VA_ARGS__);                                  \
        cerr << endl;                                       \
    } while (false);
#else
#define dbg(...)
#endif
using mint = ModInt998244353;

Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);

mint solve(int h, int w) {
    if (h % 2 == 0) return mint(0);
    int c = (w % 2 == 0) ? 2 * h : h;
    mint ans = 0;
    for (int i : iota(0, c + 1)) {
        int z = i - (c - i);
        z = (z % w + w) % w;
        if (gcd(z, w) != ((w % 2 == 0) ? 2 : 1)) continue;

        ans += comb<mint>(c, i);
    }
    return ans;
}

int main() {
    int h, w;
    sc.read(h, w);
    auto ans = solve(h, w);
    pr.writeln(ans.val());
    return 0;
}

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