結果

問題 No.2326 Factorial to the Power of Factorial to the...
ユーザー phocom
提出日時 2023-05-28 10:22:51
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 9 ms / 2,000 ms
コード長 3,838 bytes
コンパイル時間 1,158 ms
コンパイル使用メモリ 118,292 KB
最終ジャッジ日時 2025-02-13 09:32:39
ジャッジサーバーID
(参考情報)
judge4 / judge1
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ファイルパターン 結果
sample AC * 2
other AC * 20
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 #
プレゼンテーションモードにする

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#define REP(i, N) for (int i = 0; i < (int)N; i++)
#define FOR(i, a, b) for (int i = a; i < (int)b; i++)
#define ALL(x) (x).begin(), (x).end()
using namespace std;
constexpr int inf = 1 << 30;
constexpr long long llinf = 1LL << 62;
constexpr int mod = 1000000007;
using ll = long long;
template <int MOD = 1000000007>
struct Math {
vector<long long> fact, factinv, inv;
Math(int n = 100000) {
fact.resize(n + 1);
factinv.resize(n + 1);
inv.resize(n + 1);
fact[0] = fact[1] = 1;
factinv[0] = factinv[1] = 1;
inv[1] = 1;
for (int i = 2; i <= n; ++i) {
fact[i] = fact[i - 1] * i % MOD;
inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
factinv[i] = factinv[i - 1] * inv[i] % MOD;
}
}
long long C(int n, int r) {
if (n < r || n < 0 || r < 0) {
return 0;
} else {
return fact[n] * (factinv[r] * factinv[n - r] % MOD) % MOD;
}
}
long long P(int n, int r) {
if (n < r || n < 0 || r < 0) {
return 0;
} else {
return fact[n] * factinv[n - r] % MOD;
}
}
long long H(int n, int r) { return C(n + r - 1, r); }
};
namespace phc {
long long modpow(long long a, long long n) {
long long res = 1;
while (n > 0) {
if (n & 1) res = res * a % mod;
a = a * a % mod;
n >>= 1;
}
return res;
}
long long modinv(long long a) {
long long b = mod, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
u %= mod;
if (u < 0) u += mod;
return u;
}
long long gcd(long long a, long long b) { return b != 0 ? gcd(b, a % b) : a; }
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
} // namespace phc
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; }
ModInt inverse() const {
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 modint = ModInt<mod>;
int main() {
ll N, P;
cin >> N >> P;
modint ans = 0;
for (ll x = 1; x <= N; ++x) {
ll y = x;
while (y % P == 0) {
ans += 1;
y /= P;
}
}
Math<mod> m1(N);
Math<mod - 1> m2(N);
cout << (ans * phc::modpow(m1.fact[N], m2.fact[N])).x << endl;
return 0;
}
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