結果

問題 No.840 ほむほむほむら
コンテスト
ユーザー knshnb
提出日時 2019-06-15 18:49:58
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 194 ms / 4,000 ms
コード長 7,742 bytes
コンパイル時間 2,196 ms
コンパイル使用メモリ 187,292 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-19 07:21:10
合計ジャッジ時間 4,308 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 25
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define REP(i, n) for (long long i = 0, max_i = (n); i < max_i; i++)
#define REPI(i, a, b) for (long long i = (a), max_i = (b); i < max_i; i++)
#define ALL(obj) begin(obj), end(obj)
#define RALL(obj) rbegin(obj), rend(obj)
#define fi first
#define se second
using ii = pair<int, int>;
vector<ii> dirs = {
  {1, 0}, {0, 1}, {-1, 0}, {0, -1},  // 4方向
  {1, 1}, {-1, 1}, {-1, -1}, {1, -1},  // 斜め
  {0, 0},  // 自身
};
template <class T> inline bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; }
template <class T> inline bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; }
template <class T, class S> vector<T> make_vec(size_t n, S x) { return vector<T>(n, x); }
template <class T, class... Ts> auto make_vec(size_t n, Ts... ts) { return vector<decltype(make_vec<T>(ts...))>(n, make_vec<T>(ts...)); }

// debug
template <class T> ostream& operator<<(ostream& s, vector<T>& d) { REP (i, d.size()) s << d[i] << (i == d.size() - 1 ? "" : " "); return s; }
template <class T> ostream& operator<<(ostream& s, vector<vector<T>>& d) { REP (i, d.size()) s << d[i] << (i == d.size() - 1 ? "" : "\n"); return s; }
template <class T, class S> ostream& operator<<(ostream& s, pair<T, S>& p) { s << "{" << p.first << ", " << p.second << "}"; return s; }
template <class T, class S> ostream& operator<<(ostream& s, map<T, S> m) { for (auto it = m.begin(); it != m.end(); it++) { s << *it << (next(it) == m.end() ? "" : "\n"); } return s; }
template <class T, class S> ostream& operator<<(ostream& s, unordered_map<T, S> m) { for (auto it = m.begin(); it != m.end(); it++) { s << *it << (next(it) == m.end() ? "" : "\n"); } return s; }
#ifdef _MY_DEBUG
  #define dump(...) cerr << "/* " << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << endl, dump_func(__VA_ARGS__), cerr << "*/\n\n";
#else
  #define dump(...)
  #define endl "\n"
#endif
void dump_func() { cerr << endl; }
template <class Head, class... Tail> void dump_func(Head&& h, Tail&&... t) { cerr << h << (sizeof...(Tail) == 0 ? "" : ", "), dump_func(forward<Tail>(t)...); }

struct Fast { Fast() { cin.tie(0); ios::sync_with_stdio(false); } } fast;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
constexpr int MOD = 998244353;
// *************** TEMPLATE END *************** 

template <class T>
T pow(T x, int n, const T UNION = 1) {
  T ret = UNION;
  while (n) {
    if (n & 1) ret *= x;
    x *= x; n >>= 1;
  }
  return ret;
}

template <int MD>
struct ModInt {
  int x;
  static unordered_map<int, int> to_inv;
  ModInt() : x(0) {}
  ModInt(int x_) { if ((x = x_ % MD + MD) >= MD) x -= MD; }

  ModInt& operator+=(ModInt that) { if ((x += that.x) >= MD) x -= MD; return *this; }
  ModInt& operator*=(ModInt that) { x = (unsigned long long)x * that.x % MD; return *this; }
  ModInt& operator-=(ModInt that) { if ((x -= that.x) < 0) x += MD; return *this; }
  ModInt& operator/=(ModInt that) { x = (unsigned long long)x * that.inv().x % MD; return *this; }

  ModInt operator-() const { return -x < 0 ? MD - x : -x; }
  ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
  ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
  ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
  ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
  bool operator==(ModInt that) const { return x == that.x; }
  bool operator!=(ModInt that) const { return x != that.x; }
  ModInt inv() const { return to_inv.count(this->x) ? to_inv[this->x] : (to_inv[this->x] = pow(*this, MD - 2).x); }
  friend ostream& operator<<(ostream& s, ModInt<MD> a) { s << a.x; return s; }
  friend istream& operator>>(istream& s, ModInt<MD>& a) { s >> a.x; return s; }
};
template <int MD> unordered_map<int, int> ModInt<MD>::to_inv;
using mint = ModInt<MOD>;

vector<mint> fact, fact_inv;
void init_factorial(int n) {
  fact = vector<mint>(n + 1, 1);
  fact_inv = vector<mint>(n + 1);
  for (int i = 0; i < n; i++) fact[i + 1] = fact[i] * (i + 1);
  fact_inv[n] = mint(1) / fact[n];
  for (int i = n - 1; i >= 0; i--) fact_inv[i] = fact_inv[i + 1] * (i + 1);
  // for (int i = 0; i < n + 1; i++) assert(fact[i] * fact_inv[i] == 1);
}
mint comb(int n, int r) {
  return fact[n] * fact_inv[r] * fact_inv[n - r];
}

template <class T>
struct Matrix {
  vector<vector<T>> A;
  Matrix() {}
  Matrix(int n) : A(n, vector< T >(n, 0)) {}
  Matrix(const vector<vector<T>>& A) : A(A) {}
  static Matrix I(int n) {
    Matrix mat(n);
    for(int i = 0; i < n; i++) mat[i][i] = 1;
    return (mat);
  }
  int height() const { return (A.size()); }
  int width() const { return (A[0].size()); }
  vector<T>& operator[](int k) { return A[k]; }
  const vector<T>& operator[](int k) const { return (A[k]); }
  Matrix& operator+=(const Matrix &B) {
    assert(A.size() == B.A.size() && A[0].size() == B.A[0].size());
    for(int i = 0; i < A.size(); i++)
      for(int j = 0; j < A[0].size(); j++)
        (*this)[i][j] += B[i][j];
    return (*this);
  }
  Matrix &operator-=(const Matrix &B) {
    assert(A.size() == B.A.size() && A[0].size() == B.A[0].size());
    for(int i = 0; i < A.size(); i++)
      for(int j = 0; j < A[0].size(); j++)
        (*this)[i][j] -= B[i][j];
    return (*this);
  }
  Matrix &operator*=(const Matrix &B) {
    int n = height(), m = B.width(), p = width();
    assert(p == B.height());
    vector<vector<T>> C(n, vector<T>(m, 0));
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        for(int k = 0; k < p; k++)
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
    A.swap(C);
    return (*this);
  }
  Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } 
  Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
  Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } 
  vector<T> operator*(const vector<T>& x) const {
    int n = height(), m = width();
    assert(m == x.size());
    vector<T> ret(n);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        ret[i] += (*this)[i][j] * x[j];
    return ret;
  }
  friend ostream &operator<<(ostream &os, Matrix &p) {
    int n = p.height(), m = p.width();
    for(int i = 0; i < n; i++) {
      os << "[";
      for(int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }
  T determinant() {
    Matrix B(*this);
    assert(width() == height());
    T ret = 1;
    for(int i = 0; i < width(); i++) {
      int idx = -1;
      for(int j = i; j < width(); j++) {
        if(B[j][i] != 0) idx = j;
      }
      if(idx == -1) return (0);
      if(i != idx) {
        ret *= -1;
        swap(B[i], B[idx]);
      }
      ret *= B[i][i];
      T vv = B[i][i];
      for(int j = 0; j < width(); j++) {
        B[i][j] /= vv;
      }
      for(int j = i + 1; j < width(); j++) {
        T a = B[j][i];
        for(int k = 0; k < width(); k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return (ret);
  }
};

signed main() {
  int n, K; cin >> n >> K;
  auto make = [&](int a, int b, int c) {
    a %= K;
    b %= K;
    c %= K;
    return a * K * K + b * K + c;
  };
  Matrix<mint> A(K * K * K);
  REP (a, K) {
    REP (b, K) {
      REP (c, K) {
        A[make(a + 1, b, c)][make(a, b, c)] += 1;
        A[make(a, b + a, c)][make(a, b, c)] += 1;
        A[make(a, b, c + b)][make(a, b, c)] += 1;
      }
    }
  }
  vector<mint> x(K * K * K);
  x[make(0, 0, 0)] = 1;
  auto res = pow(A, n, Matrix<mint>::I(K * K * K)) * x;
  mint ans = 0;
  REP (a, K) {
    REP (b, K) {
      ans += res[make(a, b, 0)];
    }
  }
  cout << ans << endl;
}
0