Submission #41422414

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Source Code Expand

#include <cstdio>
#include <cassert>
#include <array>
#include <algorithm>
#include <complex>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <deque>
#include <bit>
#include <numeric>
#include <functional>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <memory>
#include <thread>
#include <tuple>
#include <limits>
#include <iostream>
#include <iomanip>

using namespace std;

template<unsigned int mod>
struct ModInt
{
  unsigned int val;
  ModInt() : val(0) {}
  ModInt(const ModInt<mod>& other) : val(other.val) {}
  ModInt(long long x) {
    x %= mod;
    if (x < 0) x += mod;
    val = static_cast<unsigned int>(x);
  }
  unsigned int inverse() const {
    int a = val, b = mod, x = 1, y = 0;
    while (b) {
      int q = a / b;
      int t = a % b;
      a = b;
      b = t;
      int u = x - q * y;
      x = y;
      y = u;
    }
    if (x < 0) x += mod;
    return x;
  }
  ModInt<mod>& operator +=(const ModInt<mod>& other) {
    val += other.val;
    if (val >= mod)
      val -= mod;
    return *this;
  }
  ModInt<mod>& operator -=(const ModInt<mod>& other) {
    val += mod - other.val;
    if (val >= mod)
      val -= mod;
    return *this;
  }
  ModInt<mod>& operator *=(const ModInt<mod>& other) {
    val = (unsigned long long)val * other.val % mod;
    return *this;
  }
  ModInt<mod>& operator /=(const ModInt<mod>& other) {
    val = (unsigned long long)val * other.inverse() % mod;
    return *this;
  }
  ModInt<mod> operator +(const ModInt<mod>& other) const { ModInt<mod> cp(val); cp += other; return cp; }
  ModInt<mod> operator -(const ModInt<mod>& other) const { ModInt<mod> cp(val); cp -= other; return cp; }
  ModInt<mod> operator *(const ModInt<mod>& other) const { ModInt<mod> cp(val); cp *= other; return cp; }
  ModInt<mod> operator /(const ModInt<mod>& other) const { ModInt<mod> cp(val); cp /= other; return cp; }
  bool operator ==(const ModInt<mod>& other) const { return val == other.val; }
  bool operator !=(const ModInt<mod>& other) const { return val != other.val; }
  ModInt<mod> operator +() const { return *this; }
  ModInt<mod> operator -() const { return 0 == val ? 0 : (mod - val); }
  int operator !() const { return !val; }
};

constexpr int mod = 998244353;
typedef ModInt<mod> mint;


namespace atcoder {

  namespace internal {


#ifndef _MSC_VER
    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 ||
      is_signed_int128<T>::value ||
      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;

#else

    template <class T> using is_integral = typename std::is_integral<T>;

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

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

#endif

    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;



    // @param m `1 <= m`
    // @return x mod m
    constexpr long long safe_mod(long long x, long long m) {
      x %= m;
      if (x < 0) x += m;
      return x;
  }

    // Fast modular multiplication by barrett reduction
    // Reference: https://en.wikipedia.org/wiki/Barrett_reduction
    // NOTE: reconsider after Ice Lake
    struct barrett {
      unsigned int _m;
      unsigned long long im;

      // @param m `1 <= m`
      explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

      // @return m
      unsigned int umod() const { return _m; }

      // @param a `0 <= a < m`
      // @param b `0 <= b < m`
      // @return `a * b % m`
      unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
          (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned long long y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
      }
    };

    // @param n `0 <= n`
    // @param m `1 <= m`
    // @return `(x ** n) % m`
    constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
      if (m == 1) return 0;
      unsigned int _m = (unsigned int)(m);
      unsigned long long r = 1;
      unsigned long long y = safe_mod(x, m);
      while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
      }
      return r;
    }

    // Reference:
    // M. Forisek and J. Jancina,
    // Fast Primality Testing for Integers That Fit into a Machine Word
    // @param n `0 <= n`
    constexpr bool is_prime_constexpr(int n) {
      if (n <= 1) return false;
      if (n == 2 || n == 7 || n == 61) return true;
      if (n % 2 == 0) return false;
      long long d = n - 1;
      while (d % 2 == 0) d /= 2;
      constexpr long long bases[3] = { 2, 7, 61 };
      for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
          y = y * y % n;
          t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
          return false;
        }
      }
      return true;
    }
    template <int n> constexpr bool is_prime = is_prime_constexpr(n);

    // @param b `1 <= b`
    // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
    constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
      a = safe_mod(a, b);
      if (a == 0) return { b, 0 };

      // Contracts:
      // [1] s - m0 * a = 0 (mod b)
      // [2] t - m1 * a = 0 (mod b)
      // [3] s * |m1| + t * |m0| <= b
      long long s = b, t = a;
      long long m0 = 0, m1 = 1;

      while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
      }
      // by [3]: |m0| <= b/g
      // by g != b: |m0| < b/g
      if (m0 < 0) m0 += b / s;
      return { s, m0 };
    }

    // Compile time primitive root
    // @param m must be prime
    // @return primitive root (and minimum in now)
    constexpr int primitive_root_constexpr(int m) {
      if (m == 2) return 1;
      if (m == 167772161) return 3;
      if (m == 469762049) return 3;
      if (m == 754974721) return 11;
      if (m == 998244353) return 3;
      int divs[20] = {};
      divs[0] = 2;
      int cnt = 1;
      int x = (m - 1) / 2;
      while (x % 2 == 0) x /= 2;
      for (int i = 3; (long long)(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 (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
            ok = false;
            break;
          }
        }
        if (ok) return g;
      }
    }
    template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

    // @param n `n < 2^32`
    // @param m `1 <= m < 2^32`
    // @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
    unsigned long long floor_sum_unsigned(unsigned long long n,
      unsigned long long m,
      unsigned long long a,
      unsigned long long b) {
      unsigned long long ans = 0;
      while (true) {
        if (a >= m) {
          ans += n * (n - 1) / 2 * (a / m);
          a %= m;
        }
        if (b >= m) {
          ans += n * (b / m);
          b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
      }
      return ans;
    }



#if __cplusplus >= 202002L

    using std::bit_ceil;

#else

    // @return same with std::bit::bit_ceil
    unsigned int bit_ceil(unsigned int n) {
      unsigned int x = 1;
      while (x < (unsigned int)(n)) x *= 2;
      return x;
    }

#endif

    // @param n `1 <= n`
    // @return same with std::bit::countr_zero
    int countr_zero(unsigned int n) {
#ifdef _MSC_VER
      unsigned long index;
      _BitScanForward(&index, n);
      return index;
#else
      return __builtin_ctz(n);
#endif
    }

    // @param n `1 <= n`
    // @return same with std::bit::countr_zero
    constexpr int countr_zero_constexpr(unsigned int n) {
      int x = 0;
      while (!(n & (1 << x))) x++;
      return x;
    }


    struct modint_base {};
    struct static_modint_base : modint_base {};

    template <class T> using is_modint = std::is_base_of<modint_base, T>;
    template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

  }  // namespace internal

  template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
  struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
      mint x;
      x._v = v;
      return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
      long long x = (long long)(v % (long long)(umod()));
      if (x < 0) x += umod();
      _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
      _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
      _v++;
      if (_v == umod()) _v = 0;
      return *this;
    }
    mint& operator--() {
      if (_v == 0) _v = umod();
      _v--;
      return *this;
    }
    mint operator++(int) {
      mint result = *this;
      ++* this;
      return result;
    }
    mint operator--(int) {
      mint result = *this;
      --* this;
      return result;
    }

    mint& operator+=(const mint& rhs) {
      _v += rhs._v;
      if (_v >= umod()) _v -= umod();
      return *this;
    }
    mint& operator-=(const mint& rhs) {
      _v -= rhs._v;
      if (_v >= umod()) _v += umod();
      return *this;
    }
    mint& operator*=(const mint& rhs) {
      unsigned long long z = _v;
      z *= rhs._v;
      _v = (unsigned int)(z % umod());
      return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
      assert(0 <= n);
      mint x = *this, r = 1;
      while (n) {
        if (n & 1) r *= x;
        x *= x;
        n >>= 1;
      }
      return r;
    }
    mint inv() const {
      if (prime) {
        assert(_v);
        return pow(umod() - 2);
      } else {
        auto eg = internal::inv_gcd(_v, m);
        assert(eg.first == 1);
        return eg.second;
      }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
      return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
      return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
      return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
      return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
      return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
      return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
  };

  template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
      assert(1 <= m);
      bt = internal::barrett(m);
    }
    static mint raw(int v) {
      mint x;
      x._v = v;
      return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
      long long x = (long long)(v % (long long)(mod()));
      if (x < 0) x += mod();
      _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
      _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
      _v++;
      if (_v == umod()) _v = 0;
      return *this;
    }
    mint& operator--() {
      if (_v == 0) _v = umod();
      _v--;
      return *this;
    }
    mint operator++(int) {
      mint result = *this;
      ++* this;
      return result;
    }
    mint operator--(int) {
      mint result = *this;
      --* this;
      return result;
    }

    mint& operator+=(const mint& rhs) {
      _v += rhs._v;
      if (_v >= umod()) _v -= umod();
      return *this;
    }
    mint& operator-=(const mint& rhs) {
      _v += mod() - rhs._v;
      if (_v >= umod()) _v -= umod();
      return *this;
    }
    mint& operator*=(const mint& rhs) {
      _v = bt.mul(_v, rhs._v);
      return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
      assert(0 <= n);
      mint x = *this, r = 1;
      while (n) {
        if (n & 1) r *= x;
        x *= x;
        n >>= 1;
      }
      return r;
    }
    mint inv() const {
      auto eg = internal::inv_gcd(_v, mod());
      assert(eg.first == 1);
      return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
      return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
      return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
      return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
      return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
      return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
      return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
  };
  template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

  using modint998244353 = static_modint<998244353>;
  using modint1000000007 = static_modint<1000000007>;
  using modint = dynamic_modint<-1>;

  namespace internal {

    template <class T>
    using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

    template <class T>
    using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

    template <class> struct is_dynamic_modint : public std::false_type {};
    template <int id>
    struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

    template <class T>
    using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;



    template <class mint,
      int g = internal::primitive_root<mint::mod()>,
      internal::is_static_modint_t<mint>* = nullptr>
    struct fft_info {
      static constexpr int rank2 = countr_zero_constexpr(mint::mod() - 1);
      std::array<mint, rank2 + 1> root;   // root[i]^(2^i) == 1
      std::array<mint, rank2 + 1> iroot;  // root[i] * iroot[i] == 1

      std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
      std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;

      std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
      std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;

      fft_info() {
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        iroot[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
          root[i] = root[i + 1] * root[i + 1];
          iroot[i] = iroot[i + 1] * iroot[i + 1];
        }

        {
          mint prod = 1, iprod = 1;
          for (int i = 0; i <= rank2 - 2; i++) {
            rate2[i] = root[i + 2] * prod;
            irate2[i] = iroot[i + 2] * iprod;
            prod *= iroot[i + 2];
            iprod *= root[i + 2];
          }
        }
        {
          mint prod = 1, iprod = 1;
          for (int i = 0; i <= rank2 - 3; i++) {
            rate3[i] = root[i + 3] * prod;
            irate3[i] = iroot[i + 3] * iprod;
            prod *= iroot[i + 3];
            iprod *= root[i + 3];
          }
        }
      }
    };

    template <class mint, internal::is_static_modint_t<mint>* = nullptr>
    void butterfly(std::vector<mint>& a) {
      int n = int(a.size());
      int h = internal::countr_zero((unsigned int)n);

      static const fft_info<mint> info;

      int len = 0;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
      while (len < h) {
        if (h - len == 1) {
          int p = 1 << (h - len - 1);
          mint rot = 1;
          for (int s = 0; s < (1 << len); s++) {
            int offset = s << (h - len);
            for (int i = 0; i < p; i++) {
              auto l = a[i + offset];
              auto r = a[i + offset + p] * rot;
              a[i + offset] = l + r;
              a[i + offset + p] = l - r;
            }
            if (s + 1 != (1 << len))
              rot *= info.rate2[countr_zero(~(unsigned int)(s))];
          }
          len++;
        } else {
          // 4-base
          int p = 1 << (h - len - 2);
          mint rot = 1, imag = info.root[2];
          for (int s = 0; s < (1 << len); s++) {
            mint rot2 = rot * rot;
            mint rot3 = rot2 * rot;
            int offset = s << (h - len);
            for (int i = 0; i < p; i++) {
              auto mod2 = 1ULL * mint::mod() * mint::mod();
              auto a0 = 1ULL * a[i + offset].val();
              auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
              auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
              auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
              auto a1na3imag =
                1ULL * mint(a1 + mod2 - a3).val() * imag.val();
              auto na2 = mod2 - a2;
              a[i + offset] = a0 + a2 + a1 + a3;
              a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
              a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
              a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
            }
            if (s + 1 != (1 << len))
              rot *= info.rate3[countr_zero(~(unsigned int)(s))];
          }
          len += 2;
        }
      }
    }

    template <class mint, internal::is_static_modint_t<mint>* = nullptr>
    void butterfly_inv(std::vector<mint>& a) {
      int n = int(a.size());
      int h = internal::countr_zero((unsigned int)n);

      static const fft_info<mint> info;

      int len = h;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
      while (len) {
        if (len == 1) {
          int p = 1 << (h - len);
          mint irot = 1;
          for (int s = 0; s < (1 << (len - 1)); s++) {
            int offset = s << (h - len + 1);
            for (int i = 0; i < p; i++) {
              auto l = a[i + offset];
              auto r = a[i + offset + p];
              a[i + offset] = l + r;
              a[i + offset + p] =
                (unsigned long long)(mint::mod() + l.val() - r.val()) *
                irot.val();
              ;
            }
            if (s + 1 != (1 << (len - 1)))
              irot *= info.irate2[countr_zero(~(unsigned int)(s))];
          }
          len--;
        } else {
          // 4-base
          int p = 1 << (h - len);
          mint irot = 1, iimag = info.iroot[2];
          for (int s = 0; s < (1 << (len - 2)); s++) {
            mint irot2 = irot * irot;
            mint irot3 = irot2 * irot;
            int offset = s << (h - len + 2);
            for (int i = 0; i < p; i++) {
              auto a0 = 1ULL * a[i + offset + 0 * p].val();
              auto a1 = 1ULL * a[i + offset + 1 * p].val();
              auto a2 = 1ULL * a[i + offset + 2 * p].val();
              auto a3 = 1ULL * a[i + offset + 3 * p].val();

              auto a2na3iimag =
                1ULL *
                mint((mint::mod() + a2 - a3) * iimag.val()).val();

              a[i + offset] = a0 + a1 + a2 + a3;
              a[i + offset + 1 * p] =
                (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
              a[i + offset + 2 * p] =
                (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
                irot2.val();
              a[i + offset + 3 * p] =
                (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
                irot3.val();
            }
            if (s + 1 != (1 << (len - 2)))
              irot *= info.irate3[countr_zero(~(unsigned int)(s))];
          }
          len -= 2;
        }
      }
    }

    template <class mint, internal::is_static_modint_t<mint>* = nullptr>
    std::vector<mint> convolution_naive(const std::vector<mint>& a,
      const std::vector<mint>& b) {
      int n = int(a.size()), m = int(b.size());
      std::vector<mint> ans(n + m - 1);
      if (n < m) {
        for (int j = 0; j < m; j++) {
          for (int i = 0; i < n; i++) {
            ans[i + j] += a[i] * b[j];
          }
        }
      } else {
        for (int i = 0; i < n; i++) {
          for (int j = 0; j < m; j++) {
            ans[i + j] += a[i] * b[j];
          }
        }
      }
      return ans;
    }

    template <class mint, internal::is_static_modint_t<mint>* = nullptr>
    std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
      int n = int(a.size()), m = int(b.size());
      int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
      a.resize(z);
      internal::butterfly(a);
      b.resize(z);
      internal::butterfly(b);
      for (int i = 0; i < z; i++) {
        a[i] *= b[i];
      }
      internal::butterfly_inv(a);
      a.resize(n + m - 1);
      mint iz = mint(z).inv();
      for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
      return a;
    }

  }  // namespace internal

  template <class mint, internal::is_static_modint_t<mint>* = nullptr>
  std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
    assert((mint::mod() - 1) % z == 0);

    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
  }
  template <class mint, internal::is_static_modint_t<mint>* = nullptr>
  std::vector<mint> convolution(const std::vector<mint>& a,
    const std::vector<mint>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
    assert((mint::mod() - 1) % z == 0);

    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
  }

  template <unsigned int mod = 998244353,
    class T,
    std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
  std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    using mint = static_modint<mod>;

    int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
    assert((mint::mod() - 1) % z == 0);

    std::vector<mint> a2(n), b2(m);
    for (int i = 0; i < n; i++) {
      a2[i] = mint(a[i]);
    }
    for (int i = 0; i < m; i++) {
      b2[i] = mint(b[i]);
    }
    auto c2 = convolution(std::move(a2), std::move(b2));
    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
      c[i] = c2[i].val();
    }
    return c;
  }
}

/* find (gcd, c, d) s.t. ac + bd = gcd
 * Returns (gcd, c, d). gcd can be negative if a or b is negative
 * |c| < |b/gcd|, |d| < |a/gcd| if a and b are non-multiple
 * Dependencies: none */
tuple<long long, long long, long long> extended_gcd(long long a, long long b) {
  long long s = 1, t = 0;
  long long u = 0, v = 1;
  // loop invariant: (A,B) = (input a, input b), a = s*A + t*B, b = u*A + v*B
  while (b != 0) {
    long long q = a / b;
    tie(a, b) = make_pair(b, a % b);
    // b' = A(s-uq) + B(t-vq)
    tie(s, t, u, v) = make_tuple(u, v, s - u * q, t - v * q);
  }
  return make_tuple(a, s, t);
}

/* Find x in [0,m) s.t. ax ≡ gcd(a, m) (mod m)
 * Assumption: m > 0
 * Dependencies: extended_gcd(a, b) */
long long modinverse(long long a, long long m) {
  a = a % m;
  if (a < 0) a += m;
  long long value = get<1>(extended_gcd(a, m)) % m;
  return (value < 0) ? value + m : value;
}


int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int n, K;
  long long m;
  cin >> n >> m >> K;
  if (m % K) {
    cout << "0\n";
    return 0;
  }
  // real count
  m /= K;

  vector<int> A(K, 1), R(1, 1);
  if (n - K + 1 >= 1) {
    int p = n - K + 1;
    while (p) {
      if (p % 2) {
        R = atcoder::convolution(R, A);
      }
      A = atcoder::convolution(A, A);
      p >>= 1;
    }
  }
  mint ans = 0;
  mint bin = 1;
  constexpr int TS = 2048;
  vector<mint> itree(TS * 2, 1);
  for (int i = 1; i <= n - 1; i++) {
    bin *= modinverse(i, mod);
    itree[TS + (i - 1)] = mint((m + n - i) % mod);
  }
  for (int i = TS - 1; i >= 1; i--) {
    itree[i] = itree[i * 2] * itree[i * 2 + 1];
  }
  for (int i = 0; i <= m && i < R.size(); i++) {
    mint val = R[i];
    // add rem everywhere
    long long rem = m - i;
    // binom(rem+n-1, n-1)
    val *= bin * itree[1];
    ans += val;
    if (n >= 2) {
      int pos = TS + (i % (n - 1));
      itree[pos] = rem;
      pos >>= 1;
      while (pos >= 1) {
        itree[pos] = itree[pos * 2] * itree[pos * 2 + 1];
        pos >>= 1;
      }
    }
  }
  cout << ans.val << "\n";
  return 0;
}

Submission Info

Compile Error

./Main.cpp: In function ‘int main()’:
./Main.cpp:977:49: warning: implicitly-declared ‘constexpr ModInt<998244353>& ModInt<998244353>::operator=(const ModInt<998244353>&)’ is deprecated [-Wdeprecated-copy]
  977 |     itree[TS + (i - 1)] = mint((m + n - i) % mod);
      |                                                 ^
./Main.cpp:35:3: note: because ‘ModInt<998244353>’ has user-provided ‘ModInt<mod>::ModInt(const ModInt<mod>&) [with unsigned int mod = 998244353]’
   35 |   ModInt(const ModInt<mod>& other) : val(other.val) {}
      |   ^~~~~~
./Main.cpp:980:46: warning: implicitly-declared ‘constexpr ModInt<998244353>& ModInt<998244353>::operator=(const ModInt<998244353>&)’ is deprecated [-Wdeprecated-copy]
  980 |     itree[i] = itree[i * 2] * itree[i * 2 + 1];
      |                                              ^
./Main.cpp:35:3: note: because ‘ModInt<998244353>’ has user-provided ‘ModInt<mod>::ModInt(const ModInt<mod>&) [with unsigned int mod = 998244353]’
   35 |   ModInt(const ModInt<mod>& other) : val(other.val) {}
      |   ^~~~~~
./Main.cpp:982:31: warning: comparison of integer expressions of different signedness: ‘int’ and ‘std::vector<int>::size_type’ {aka ‘long unsigned int’} [-Wsign-compare]
  982 |   for (int i = 0; i <= m && i < R.size(); i++) {
      |                             ~~^~~~~~~~~~
./Main.cpp:991:20: warning: implicitly-declared ‘constexpr ModInt<998244353>& ModInt<998244353>::operator=(const ModInt<998244353>&)’ is deprecated [-Wdeprecated-copy]
  991 |       itree[pos] = rem;
      |                    ^~~
./Main.cpp:35:3: note: because ‘ModInt<998244353>’ has user-provided ‘ModInt<mod>::ModInt(const ModInt<mod>&) [with unsigned int mod = 998244353]’
   35 |   ModInt(const ModInt<mod>& other) : val(other.val) {}
      |   ^~~~~~
./Main.cpp:994:56: warning: implicitly-declared ‘constexpr ModInt<998244353>& ModInt<998244353>::operator=(const ModInt<998244353>&)’ is deprecated [-Wdeprecated-copy]
  994 |         itree[pos] = itree...

Judge Result