結果

問題 No.2857 Div Array
ユーザー 👑 emthrmemthrm
提出日時 2024-08-25 14:08:02
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 27 ms / 2,000 ms
コード長 7,604 bytes
コンパイル時間 3,116 ms
コンパイル使用メモリ 262,280 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-08-25 14:08:07
合計ジャッジ時間 4,366 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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ファイルパターン 結果
other AC * 30
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <unsigned int M>
struct MInt {
  unsigned int v;

  constexpr MInt() : v(0) {}
  constexpr MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
  static constexpr MInt raw(const int x) {
    MInt x_;
    x_.v = x;
    return x_;
  }

  static constexpr int get_mod() { return M; }
  static constexpr void set_mod(const int divisor) {
    assert(std::cmp_equal(divisor, M));
  }

  static void init(const int x) {
    inv<true>(x);
    fact(x);
    fact_inv(x);
  }

  template <bool MEMOIZES = false>
  static MInt inv(const int n) {
    // assert(0 <= n && n < M && std::gcd(n, M) == 1);
    static std::vector<MInt> inverse{0, 1};
    const int prev = inverse.size();
    if (n < prev) return inverse[n];
    if constexpr (MEMOIZES) {
      // "n!" and "M" must be disjoint.
      inverse.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        inverse[i] = -inverse[M % i] * raw(M / i);
      }
      return inverse[n];
    }
    int u = 1, v = 0;
    for (unsigned int a = n, b = M; b;) {
      const unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }

  static MInt fact(const int n) {
    static std::vector<MInt> factorial{1};
    if (const int prev = factorial.size(); n >= prev) {
      factorial.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        factorial[i] = factorial[i - 1] * i;
      }
    }
    return factorial[n];
  }

  static MInt fact_inv(const int n) {
    static std::vector<MInt> f_inv{1};
    if (const int prev = f_inv.size(); n >= prev) {
      f_inv.resize(n + 1);
      f_inv[n] = inv(fact(n).v);
      for (int i = n; i > prev; --i) {
        f_inv[i - 1] = f_inv[i] * i;
      }
    }
    return f_inv[n];
  }

  static MInt nCk(const int n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
                                  fact_inv(n - k) * fact_inv(k));
  }
  static MInt nPk(const int n, const int k) {
    return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
  }
  static MInt nHk(const int n, const int k) {
    return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
  }

  static MInt large_nCk(long long n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    inv<true>(k);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) {
      res *= inv(i) * n--;
    }
    return res;
  }

  constexpr MInt pow(long long exponent) const {
    MInt res = 1, tmp = *this;
    for (; exponent > 0; exponent >>= 1) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
    }
    return res;
  }

  constexpr MInt& operator+=(const MInt& x) {
    if ((v += x.v) >= M) v -= M;
    return *this;
  }
  constexpr MInt& operator-=(const MInt& x) {
    if ((v += M - x.v) >= M) v -= M;
    return *this;
  }
  constexpr MInt& operator*=(const MInt& x) {
    v = (unsigned long long){v} * x.v % M;
    return *this;
  }
  MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }

  constexpr auto operator<=>(const MInt& x) const = default;

  constexpr MInt& operator++() {
    if (++v == M) [[unlikely]] v = 0;
    return *this;
  }
  constexpr MInt operator++(int) {
    const MInt res = *this;
    ++*this;
    return res;
  }
  constexpr MInt& operator--() {
    v = (v == 0 ? M - 1 : v - 1);
    return *this;
  }
  constexpr MInt operator--(int) {
    const MInt res = *this;
    --*this;
    return res;
  }

  constexpr MInt operator+() const { return *this; }
  constexpr MInt operator-() const { return raw(v ? M - v : 0); }

  constexpr MInt operator+(const MInt& x) const { return MInt(*this) += x; }
  constexpr MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
  constexpr MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt& x) const { return MInt(*this) /= x; }

  friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
    return os << x.v;
  }
  friend std::istream& operator>>(std::istream& is, MInt& x) {
    long long v;
    is >> v;
    x = MInt(v);
    return is;
  }
};
using ModInt = MInt<MOD>;

template <typename T>
struct Matrix {
  explicit Matrix(const int m, const int n, const T def = 0)
      : data(m, std::vector<T>(n, def)) {}

  int nrow() const { return data.size(); }
  int ncol() const { return data.empty() ? 0 : data.front().size(); }

  Matrix pow(long long exponent) const {
    const int n = nrow();
    Matrix<T> res(n, n, 0), tmp = *this;
    for (int i = 0; i < n; ++i) {
      res[i][i] = 1;
    }
    for (; exponent > 0; exponent >>= 1) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
    }
    return res;
  }

  inline const std::vector<T>& operator[](const int i) const { return data[i]; }
  inline std::vector<T>& operator[](const int i) { return data[i]; }

  Matrix& operator=(const Matrix& x) = default;

  Matrix& operator+=(const Matrix& x) {
    const int m = nrow(), n = ncol();
    for (int i = 0; i < m; ++i) {
      for (int j = 0; j < n; ++j) {
        data[i][j] += x[i][j];
      }
    }
    return *this;
  }

  Matrix& operator-=(const Matrix& x) {
    const int m = nrow(), n = ncol();
    for (int i = 0; i < m; ++i) {
      for (int j = 0; j < n; ++j) {
        data[i][j] -= x[i][j];
      }
    }
    return *this;
  }

  Matrix& operator*=(const Matrix& x) {
    const int m = nrow(), l = ncol(), n = x.ncol();
    std::vector<std::vector<T>> res(m, std::vector<T>(n, 0));
    for (int i = 0; i < m; ++i) {
      for (int k = 0; k < l; ++k) {
        for (int j = 0; j < n; ++j) {
          res[i][j] += data[i][k] * x[k][j];
        }
      }
    }
    data.swap(res);
    return *this;
  }

  Matrix operator+(const Matrix& x) const { return Matrix(*this) += x; }
  Matrix operator-(const Matrix& x) const { return Matrix(*this) -= x; }
  Matrix operator*(const Matrix& x) const { return Matrix(*this) *= x; }

 private:
  std::vector<std::vector<T>> data;
};

template <typename T>
std::vector<std::tuple<T, T, T>> enumerate_quotients(const T n) {
  std::vector<std::tuple<T, T, T>> quotients;
  for (T l = 1; l <= n;) {
    const T quotient = n / l, r = n / quotient + 1;
    quotients.emplace_back(l, r, quotient);
    l = r;
  }
  return quotients;
}

int main() {
  int n, m, k; cin >> n >> m >> k;
  const auto quotients = enumerate_quotients(m);
  const int q = quotients.size();
  Matrix<ModInt> dp(q, q, 0);
  REP(i, q) REP(j, q) {
    if (abs(get<2>(quotients[i]) - get<2>(quotients[j])) <= k) {
      dp[j][i] = get<1>(quotients[j]) - get<0>(quotients[j]);
    }
  }
  dp = dp.pow(n - 1);
  ModInt ans = 0;
  REP(i, q) REP(j, q) ans += dp[i][j] * (get<1>(quotients[j]) - get<0>(quotients[j]));
  cout << ans << '\n';
  return 0;
}
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