結果

問題 No.3187 Mingle
コンテスト
ユーザー hos.lyric
提出日時 2025-06-20 22:36:58
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2,143 ms / 2,500 ms
コード長 5,378 bytes
コンパイル時間 1,167 ms
コンパイル使用メモリ 112,960 KB
実行使用メモリ 12,544 KB
最終ジャッジ日時 2025-09-07 07:04:30
合計ジャッジ時間 47,762 ms
ジャッジサーバーID
（参考情報） 		judge2 / 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 * 30
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 <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <chrono>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#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; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
// Barrett
struct ModInt {
  static unsigned M;
  static unsigned long long NEG_INV_M;
  static void setM(unsigned m) { M = m; NEG_INV_M = -1ULL / M; }
  unsigned x;
  ModInt() : x(0U) {}
  ModInt(unsigned x_) : x(x_ % M) {}
  ModInt(unsigned long long x_) : x(x_ % M) {}
  ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  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) {
    const unsigned long long y = static_cast<unsigned long long>(x) * a.x;
    const unsigned long long q = static_cast<unsigned long long>((static_cast<unsigned __int128>(NEG_INV_M) * y) >> 64);
    const unsigned long long r = y - M * q;
    x = r - M * (r >= 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; }
};
unsigned ModInt::M;
unsigned long long ModInt::NEG_INV_M;
// !!!Use ModInt::setM!!!
////////////////////////////////////////////////////////////////////////////////

using Mint = ModInt;


// floor(n/x) = k
// <=>  k <= n/x < k+1
// <=>  n/(k+1) < x <= n/k
// <=>  floor(n/(k+1)) < x <= floor(n/k)
template <class T, class F> void doFloors(T n, F fun) {
  assert(n >= 1);
  for (T a = 0, b; a < n; a = b) {
    const T k = n / (a + 1);
    b = n / k;
    // (a, b]: k
    fun(a, b, k);
  }
}


constexpr int K = 500;
vector<Mint> dpSums[K + 1];

int main() {
  int N, P;
  for (; ~scanf("%d%d", &N, &P); ) {
    Mint::setM(P);
    
    vector<Mint> dp(N + 1, 0);
    for (int q = 1; q <= K; ++q) dpSums[q].assign(N / q + 1, 0);
    for (int n = 3; n <= N; ++n) {
//cerr<<"n = "<<n<<", dpSums = "<<dpSums<<endl;
      vector<int> ds;
      for (int q = 1; q <= K; ++q) {
        int a = n / (q + 1);
        int b = n / q;
        if (a >= b) continue;
        if (n % b == 0) {
          ds.push_back(b);
          --b;
        }
        if (a >= b) continue;
        dp[n] += (dpSums[q][b] - dpSums[q][a]);
      }
      for (int m = 1, lim = n / (K + 1); m <= lim; ++m) {
        if (n % m == 0) {
          ds.push_back(m);
        } else {
          dp[n] += dp[n - n % m];
        }
      }
      dp[n] += n;
      dp[n] /= (n - (int)ds.size());
      for (const int d : ds) if (d <= K) dpSums[d][n / d] = dpSums[d][n / d - 1] + dp[n];
    }
    printf("%u\n", dp[N].x);
  }
  return 0;
}
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