結果
問題 |
No.8123 Calculated N !
|
ユーザー |
👑 |
提出日時 | 2025-04-01 21:55:59 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 133 ms / 2,000 ms |
コード長 | 6,376 bytes |
コンパイル時間 | 1,494 ms |
コンパイル使用メモリ | 117,536 KB |
実行使用メモリ | 7,720 KB |
最終ジャッジ日時 | 2025-04-01 21:56:03 |
合計ジャッジ時間 | 3,512 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 |
ソースコード
#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") //////////////////////////////////////////////////////////////////////////////// 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 = 1000000007; using Mint = ModInt<MO>; inline long long divide(long long a, int b) { return a / b; } inline long long divide(long long a, long long b) { return a / b; } Int N; int sqrtN; vector<int> small0; vector<Int> large0; inline Int pi0(Int n) { return (n <= sqrtN) ? small0[n] : large0[divide(N, n)]; } int primesLen; vector<int> primes; void build() { sqrtN = sqrt(static_cast<double>(N)); small0.assign(sqrtN + 1, 0); for (int k = 1; k <= sqrtN; ++k) { small0[k] = k; } large0.assign(sqrtN + 1, 0); for (int l = 1; l <= sqrtN; ++l) { const Int n = divide(N, l); large0[l] = n; } // \sum_{p<=n} f(p) for n = floor(N/*) // f: completely multiplicative // g(p, n) := \sum[1<=x<=n] [x: prime || lpf(x) > p] f(x) // g(1, n) = \sum[1<=x<=n] f(x) (need to be computed quickly) // for p: prime: // g(p, n) = | g(p-1, n) (n < p^2) // | g(p-1, n) - f(p) (g(p-1, n/p) - g(p-1, p-1)) (n >= p^2) // O(N^(3/4) / log(N)) time, O(N^(1/2)) space for (int p = 2; p <= sqrtN; ++p) if (small0[p - 1] < small0[p]) { const int g0 = small0[p - 1]; const int snp = sqrtN / p; const int psnp = p * snp; const long long np = divide(N, p); const int limL = min<long long>(divide(np, p), sqrtN); for (int l = 1; l <= snp; ++l) { const int pl = p * l; large0[l] -= (large0[pl] - g0); } for (int l = snp + 1; l <= limL; ++l) { const int npl = divide(np, l); large0[l] -= (small0[npl] - g0); } if (snp >= p) { for (int r = sqrtN - psnp; r >= 0; --r) { small0[psnp + r] -= (small0[snp] - g0); } for (int k = snp; --k >= p; ) for (int r = p; --r >= 0; ) { small0[p * k + r] -= (small0[k] - g0); } } } for (int k = 1; k <= sqrtN; ++k) { small0[k] -= 1; } for (int l = 1; l <= sqrtN; ++l) { large0[l] -= 1; } primesLen = small0[sqrtN]; primes.resize(primesLen); for (int p = 2; p <= sqrtN; ++p) if (small0[p - 1] < small0[p]) { primes[small0[p - 1]] = p; } } int main() { for (; ~scanf("%lld", &N); ) { build(); cerr<<"pi(N) = "<<pi0(N)<<endl; Mint ans = 1; for (int k = 1; k <= sqrtN; ++k) { const Int res = pi0(N / k) - pi0(N / (k + 1)); ans *= Mint(k + 1).pow(res); } const Int lim = N / (sqrtN + 1); for (const int p : primes) { Int e = 0; for (Int n = N; n /= p; ) e += n; // if(N<=10)cerr<<p<<": "<<e<<endl; if (p > lim) ans /= (N / p + 1); ans *= (e + 1); } printf("%u\n", ans.x); } return 0; }