結果

問題 No.8123 Calculated N !
コンテスト
ユーザー HoyHoyCharhang
提出日時 2025-08-16 00:47:11
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,862 ms / 2,000 ms
コード長 3,715 bytes
コンパイル時間 3,080 ms
コンパイル使用メモリ 284,088 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-08-16 00:47:34
合計ジャッジ時間 22,393 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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ファイルパターン 結果
sample AC * 6
other AC * 16
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>
#define fi first
#define se second
#define rep(i,s,n) for (int i = (s); i < (n); ++i)
#define rrep(i,n,g) for (int i = (n)-1; i >= (g); --i)
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define len(x) (int)(x).size()
#define dup(x,y) (((x)+(y)-1)/(y))
#define pb push_back
#define eb emplace_back
#define Field(T) vector<vector<T>>
using namespace std;
using ll = long long;
using ull = unsigned long long;
template<typename T> using pq = priority_queue<T,vector<T>,greater<T>>;
using P = pair<int,int>;
template<class T>bool chmax(T&a,T b){if(a<b){a=b;return 1;}return 0;}
template<class T>bool chmin(T&a,T b){if(b<a){a=b;return 1;}return 0;}

template< int mod >
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    assert(x);
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using i64 = long long;
static inline i64 my_div(i64 n, i64 p) { return double(n) / p; };
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) i64
prime_counting(i64 N) {
  i64 N2 = sqrt(N);
  i64 NdN2 = my_div(N, N2);

  vector<i64> hl(NdN2);
  for (int i = 1; i < NdN2; i++) hl[i] = my_div(N, i) - 1;

  vector<int> hs(N2 + 1);
  iota(begin(hs), end(hs), -1);

  for (int x = 2, pi = 0; x <= N2; ++x) {
    if (hs[x] == hs[x - 1]) continue;
    i64 x2 = i64(x) * x;
    i64 imax = min<i64>(NdN2, my_div(N, x2) + 1);
    i64 ix = x;
    for (i64 i = 1; i < imax; ++i) {
      hl[i] -= (ix < NdN2 ? hl[ix] : hs[my_div(N, ix)]) - pi;
      ix += x;
    }
    for (int n = N2; n >= x2; n--) {
      hs[n] -= hs[my_div(n, x)] - pi;
    }
    ++pi;
  }
  return hl[1];
}

using mint = ModInt<1000000007>;

int main() {
  ll n;
  cin >> n;
  ll s = sqrt(n)+300000;
  mint ans = 1;
  if (s < n) {
    ll k = prime_counting(n);
    rep(cnt,2,s) {
      ll nk = prime_counting(max(n/cnt, s));
      ans *= mint(cnt).pow(k-nk);
      if (n/cnt <= s) break;
      k = nk;
    }
  }
  vector<int> p(s+1, 1);
  p[0] = p[1] = 0;
  rep(i,2,s+1) {
    if (p[i]) {
      for (int j = i*2; j <= s; j += i) p[j] = 0;
    }
  }
  rep(i,0,min(s+1, n+1)) if (p[i]) {
    mint b = 1;
    ll x = n;
    while(x > 0) {
      x /= i;
      b += x;
    }
    ans *= b;
  }
  cout << ans << endl;
  return 0;
}
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