結果

問題 No.2996 Floor Sum
コンテスト
ユーザー hos.lyric
提出日時 2024-12-21 00:18:27
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 378 ms / 5,000 ms
コード長 7,544 bytes
コンパイル時間 955 ms
コンパイル使用メモリ 106,316 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-12-21 18:07:09
合計ジャッジ時間 2,355 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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 * 2
other AC * 12
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 # 

// https://loj.ac/p/138

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;

constexpr int LIM_INV = 110;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM_INV; ++i) {
    inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
  }
  fac[0] = invFac[0] = 1;
  for (int i = 1; i < LIM_INV; ++i) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(Int n, Int k) {
  if (n < 0) {
    if (k >= 0) {
      return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
    } else {
      return 0;
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM_INV);
      return fac[n] * invFac[k] * invFac[n - k];
    } else {
      return 0;
    }
  }
}


template <class S, class T> T pathUnder(S m, S a, S b, S n, T e, T x, T y) {
  assert(m >= 1); assert(a >= 0); assert(b >= 0); assert(n >= 0);
  S c = (a * n + b) / m;
  T pre = e, suf = e;
  for (; ; ) {
    const S p = a / m; a %= m; x = x * y.pow(p);
    const S q = b / m; b %= m; pre = pre * y.pow(q);
    c -= (p * n + q);
    if (c == 0) return pre * x.pow(n) * suf;
    const S d = (m * c - b - 1) / a + 1;
    suf = y * x.pow(n - d) * suf;
    b = m - b - 1 + a; swap(m, a); n = c - 1; c = d; swap(x, y);
  }
}


constexpr int MAX = 11;
Mint bn[MAX][MAX];

int K, L;

struct Data {
  Mint dx, dy;
  Mint sum[MAX][MAX];
  Data() : dx(0), dy(0), sum{} {}
  friend Data operator*(const Data &a, const Data &b) {
    Data c;
    c.dx = a.dx + b.dx;
    c.dy = a.dy + b.dy;
    for (int k = 0; k <= K; ++k) for (int l = 0; l <= L; ++l) {
      c.sum[k][l] += a.sum[k][l];
    }
    Mint tmp[MAX][MAX];
    for (int k = 0; k <= K; ++k) for (int l = 0; l <= L; ++l) {
      Mint pw = 1;
      for (int kk = 0; kk <= k; ++kk) {
        tmp[k][l] += bn[k][kk] * pw * b.sum[k - kk][l];
        pw *= a.dx;
      }
    }
    for (int k = 0; k <= K; ++k) for (int l = 0; l <= L; ++l) {
      Mint pw = 1;
      for (int ll = 0; ll <= l; ++ll) {
        c.sum[k][l] += bn[l][ll] * pw * tmp[k][l - ll];
        pw *= a.dy;
      }
    }
    return c;
  }
  Data pow(Int e) const {
    Data a = *this, b;
    for (; ; a = a * a) {
      if (e & 1) b = b * a;
      if (!(e >>= 1)) return b;
    }
  }
};


// floor(a / b)
template <class T> T divFloor(T a, T b) {
  return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}

// ceil(a / b)
template <class T> T divCeil(T a, T b) {
  return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}


int main() {
  prepare();
  for (int n = 0; n < MAX; ++n) {
    bn[n][0] = bn[n][n] = 1;
    for (int k = 1; k < n; ++k) {
      bn[n][k] = bn[n - 1][k - 1] + bn[n - 1][k];
    }
  }
  
  for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
    Int N, A, B, C;
    // scanf("%lld%lld%lld%lld%d%d", &N, &A, &B, &C, &K, &L);
    scanf("%d%d%lld%lld%lld%lld", &K, &L, &N, &C, &A, &B);
    
    bool neg = false;
    if (A < 0) {
      neg = true;
      B += A * N;
      A = -A;
    }
    Int BQ = B / C;
    Int BR = B % C;
    if (BR < 0) {
      BQ -= 1;
      BR += C;
    }
// cerr<<N<<" "<<A<<" "<<make_pair(BQ,BR)<<" "<<C<<" "<<K<<" "<<L<<endl;
    
    Data X, Y;
    X.dx = 1;
    X.sum[0][0] = 1;
    Y.dy = 1;
    const Data res = pathUnder<__int128>(C, A, BR, N + 1, Data(), X, Y);
    // printf("%u\n", res.sum[K][L].x);
    Mint ans = 0;
    if (neg) {
      // (N-i)^K (BQ+j)^L
      for (int k = 0; k <= K; ++k) for (int l = 0; l <= L; ++l) {
        ans += bn[K][k] * bn[L][l] * Mint(N).pow(K - k) * Mint(BQ).pow(L - l) * (k&1?-1:+1) * res.sum[k][l];
      }
    } else {
      // i^K (BQ+j)^L
      for (int l = 0; l <= L; ++l) {
        ans += bn[L][l] * Mint(BQ).pow(l) * res.sum[K][L - l];
      }
    }
    printf("%u\n", ans.x);
  }
#ifndef LOCAL
  break;
#endif
  }
  return 0;
}
0