#876042 (C++17) No.2326 Factorial to the Power of Factorial to the...

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結果

問題	No.2326 Factorial to the Power of Factorial to the...
ユーザー	daris
提出日時	2023-05-30 17:02:10
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	9 ms / 2,000 ms
コード長	11,843 bytes
コンパイル時間	2,321 ms
コンパイル使用メモリ	212,848 KB
実行使用メモリ	5,632 KB
最終ジャッジ日時	2024-06-08 20:16:46
合計ジャッジ時間	3,156 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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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	9 ms 5,376 KB
testcase_02	AC	4 ms 5,376 KB
testcase_03	AC	6 ms 5,376 KB
testcase_04	AC	5 ms 5,376 KB
testcase_05	AC	4 ms 5,376 KB
testcase_06	AC	5 ms 5,376 KB
testcase_07	AC	7 ms 5,632 KB
testcase_08	AC	8 ms 5,632 KB
testcase_09	AC	8 ms 5,376 KB
testcase_10	AC	3 ms 5,376 KB
testcase_11	AC	3 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	5 ms 5,376 KB
testcase_14	AC	6 ms 5,376 KB
testcase_15	AC	3 ms 5,376 KB
testcase_16	AC	2 ms 5,376 KB
testcase_17	AC	7 ms 5,376 KB
testcase_18	AC	3 ms 5,376 KB
testcase_19	AC	3 ms 5,376 KB
testcase_20	AC	2 ms 5,376 KB
testcase_21	AC	2 ms 5,376 KB

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ソースコード

raw source code

#ifdef INCLUDED_MAIN

const int mod = mod2;
using mint = ModInt<mod>;

// 階乗・組合せの逆元
class FactorialMod {
	void calc_inverse() {
		inverse[0] = 0;
		inverse[1] = 1;
		for (int i = 2; i < max_num + 1; i++) {
			inverse[i] = mod - ((mod / i) * inverse[mod % i] % mod);
		}
	}
	void calc_factorial_inverse() {
		factorial[0] = factorial_inverse[0] = 1;
		for (int i = 1; i < max_num + 1; i++) {
			factorial[i] = (factorial[i - 1] * i) % mod;
			factorial_inverse[i] = (factorial_inverse[i - 1] * inverse[i]) % mod;
		}
	}
public:
	int max_num;
	int mod;
	vector<ll> inverse;
	vector<ll> factorial; // % mod
	vector<ll> factorial_inverse;
	FactorialMod(int _max_num, const int& _mod) {
		max_num = _max_num; // n
		mod = _mod;
		inverse = vector<ll>(max_num + 1);
		factorial = vector<ll>(max_num + 1);
		factorial_inverse = vll(max_num + 1);
		calc_inverse();
		calc_factorial_inverse();
	}
	// nHk
	ll conbination_mod(int n, int k) {
		if (min(n, k) < 0 || max(n, k) > max_num || k > n) return 0;
		return (((factorial[n] * factorial_inverse[k]) % mod) * factorial_inverse[n - k]) % mod;
	}
	// nHk 重複組合せ
	ll multi_choose_mod(int n, int k) {
		return conbination_mod(n + k - 1, k);
	}
};

int main() {
	charm();

	ll n, p;
	cin >> n >> p;
	mint k = 0;
	ll q = p;
	while (n >= q) {
		k += n / q;
		q *= p;
	}
	FactorialMod a(n, mod);
	mint b = a.factorial[n];
	ll c = 1;
	rep(i, 1, n + 1) {
		c *= i;
		c %= mod - 1;
	}
	print(k * b.power(c));




	return 0;
}

/*
 *
 */

#else
//#define _GLIBCXX_DEBUG
//#include "typename.hpp"
#include "bits/stdc++.h"

#define overload4(_1, _2, _3, _4, name, ...) name
#define each1(i, a) for (auto&& i : a)
#define each2(i, j, a) for (auto&& [i, j] : a)
#define each3(i, j, k, a) for (auto&& [i, j, k] : a)
#define each(...) overload4(__VA_ARGS__, each3, each2, each1)(__VA_ARGS__)
#define all1(v) (v).begin(), (v).end()
#define all2(v, b) (v).begin(), (v).begin() + b
#define all3(v, a, b) (v).begin() + a, (v).begin() + b
#define all4(v, a, b, c) (v).begin() + a, (v).begin() + b, c
#define all(...) overload4(__VA_ARGS__, all4, all3, all2, all1)(__VA_ARGS__)
#define rall(v) (v).rbegin(), (v).rend()
#define rep(i, j, n) for (ll i = j; i < (ll)(n) ; i++)
#define rrep(i, j, n) for (ll i = ll(n) - 1; j <= i; i--)

using namespace std;

template<class T> using V = vector<T>;
template<class T> using VV = V<V<T>>;
template<class T, class Ta> using P = pair<T, Ta>;
template<class T> using PQ = priority_queue<T>;
template<class T> using PQgre = priority_queue<T, V<T>, greater<T>>;

using ll = long long;
using ld = long double;
//using LL = __int128;
using pii = pair<int, int>;
using psi = pair<string, int>;
using pll = pair<ll, ll>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using vb = V<bool>;
using vi = V<int>;
using vd = V<double>;
using vc = V<char>;
using vs = V<string>;
using vvb = V<vb>;
using vll = V<ll>;
using vld = V<ld>;
using vvi = V<vi>;
using vvd = V<vd>;
using vvll = V<vll>;
using vvld = V<vld>;
using vvc = V<vc>;
using vpii = V<pii>;
using vpll = V<pll>;
using vpil = V<pil>;
using vpli = V<pli>;

const int inf = 1ll << 30;
const ll infl = 1ll << 60;
const double pi = acos(-1.0);
const int mod1 = 998244353;
const int mod2 = 1000000007;
const int mod3 = 1000000009;
const vector<int> dx = { 1, 1, 0, -1, -1, -1, 0, 1 };
const vector<int> dy = { 0, 1, 1, 1, 0, -1, -1, -1 };
//const vector<pair<int, int>> delta = { { 1, 0 }, { 1, 1 }, { 0, 1 }, { -1, 1 }, { -1, 0 }, { -1, -1 }, { 0, -1 }, { 1, -1 } };

// prototype
template<typename T, typename Ta> istream& operator>>(istream& is, pair<T, Ta>& p);
template<typename T> istream& operator>>(istream& is, vector<T>& v);
template<typename T> istream& operator>>(istream& is, vector<vector<T>>& v);
//istream& operator>>(istream& is, __int128& x);
template<class T> void input(T& a);
template<class T, class... Ts> void input(T& a, Ts&... b);

template<typename T, typename Ta> istream& operator>>(istream& is, pair<T, Ta>& p) {
	is >> p.first >> p.second;
	return is;
}
template<typename T> istream& operator>>(istream& is, vector<T>& v) {
	for (auto&& c : v) is >> c;
	return is;
}
template<typename T> istream& operator>>(istream& is, vector<vector<T>>& v) {
	for (auto&& c : v) is >> c;
	return is;
}
/*
istream& operator>>(istream& is, __int128& x) {
  x = 0;
  string s;
  is >> s;
  bool res = s[0] == '-';
  for (size_t i = (res ? 1 : 0); i < s.size(); i++) {
	x *= 10;
	x += s[i] - '0';
  }
  if (res) x = -x;
  return is;
}
*/
template<class T> void input(T& a) {
	cin >> a;
}
template<class T, class... Ts> void input(T& a, Ts&... b) {
	cin >> a;
	input(b...);
}

// prototype
template<typename T, typename Ta> ostream& operator<<(ostream& os, const pair<T, Ta>& p);
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v);
template<typename T> ostream& operator<<(ostream& os, const vector<vector<T>>& v);
template<typename T, typename Ta> ostream& operator<<(ostream& os, const map<T, Ta>& mp);
template<typename T> ostream& operator<<(ostream& os, const set<T>& s);
template<typename T> ostream& operator<<(ostream& os, const multiset<T>& ms);
template<typename T, size_t... index> void printTuple(ostream& os, const T& tp, index_sequence<index...>, size_t n);
template<typename T> void forTuple(ostream& os, const T& tp);
template<typename ...T> ostream& operator<<(ostream& os, const tuple<T...>& tp);
//ostream& operator<<(ostream& os, const __int128& x);
void print();
template<class T> void print(const T& a);
template<class T, class... Ts> void print(const T& a, const Ts&... b);

template<typename T, typename Ta> ostream& operator<<(ostream& os, const pair<T, Ta>& p) {
	os << "{ " << p.first << ", " << p.second << " }";
	return os;
}
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
	os << "[ ";
	for (size_t i = 0; i < v.size(); i++) {
		os << v[i] << (i == v.size() - 1 ? "" : ", ");
	}
	return os << " ]";
}
template<typename T> ostream& operator<<(ostream& os, const vector<vector<T>>& v) {
	os << "[\n";
	for (size_t i = 0; i < v.size(); i++) {
		os << "[ ";
		for (size_t j = 0; j < v[i].size(); j++) {
			os << v[i][j] << (j == v[i].size() - 1 ? "" : ", ");
		}
		os << " ]";
		os << (i == v.size() - 1 ? "" : "\n");
	}
	return os << "\n]";
}
template<typename T, typename Ta>
ostream& operator<<(ostream& os, const map<T, Ta>& mp) {
	os << "{ ";
	auto it = mp.begin();
	while (it != mp.end()) {
		os << (it == mp.begin() ? "" : ", ") << *it;
		it++;
	}
	return os << " }";
}
template<typename T> ostream& operator<<(ostream& os, const set<T>& s) {
	os << "{ ";
	auto itr = s.begin();
	while (itr != s.end()) {
		os << (itr == s.begin() ? "" : ", ") << *itr;
		itr++;
	}
	return os << " }";
}
template<typename T>
ostream& operator<<(ostream& os, const multiset<T>& ms) {
	os << "{ ";
	auto itr = ms.begin();
	while (itr != ms.end()) {
		os << (itr == ms.begin() ? "" : ", ") << *itr;
		itr++;
	}
	return os << " }";
}
template<typename T, size_t... index> void printTuple(ostream& os, const T& tp, index_sequence<index...>, size_t n) {
	using swallow = vector<int>;
	(void)swallow
	{
		(os << get<index>(tp) << (index == n - 1 ? "" : ", "), 0)...
	};
}
template<typename T> void forTuple(ostream& os, const T& tp) {
	constexpr size_t n = tuple_size_v<T>;
	printTuple(os, tp, make_index_sequence<n>{}, n);
}
template<typename ...T> ostream& operator<<(ostream& os, const tuple<T...>& tp) {
	os << "{ ";
	forTuple(os, tp);
	return os << " }";
}
/*
ostream& operator<<(ostream& os, const __int128& x) {
  __int128 tmp = x;
  if (tmp == 0) return os << 0;
  if (tmp < 0) {
	os << '-';
	tmp = -tmp;
  }
  vector<int> ret;
  while (tmp) {
	ret.emplace_back(tmp % 10);
	tmp /= 10;
  }
  reverse(ret.begin(), ret.end());
  for (auto&& i : ret) os << i;
  return os;
}
*/
void print() {
	cout << '\n';
}
template<class T> void print(const T& a) {
	cout << a << '\n';
}
template<class T, class... Ts> void print(const T& a, const Ts&... b) {
	cout << a; (cout << ... << (cout << ' ', b));
	cout << '\n';
	//{ cout << a << ' '; print(b...); }
}

void charm() {
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	cout << fixed << setprecision(15);
}

template<typename T>
bool chmax(T& a, const T& b) {
	if (a < b) {
		a = b;
		return true;
	}
	return false;
}

template<typename T>
bool chmin(T& a, const T& b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}

template<typename T>
vector<tuple<T>> zip(vector<T>& v) {
	vector<tuple<T>> vt(v.size());
	for (size_t i = 0; i < v.size(); i++) vt[i] = make_tuple(v[i]);
	return vt;
}

template<typename T, typename... Ts>
auto zip(vector<T>& v, Ts&&... vs) {
	auto vt = zip(v);
	auto vts = zip(vs...);
	size_t m = min(vt.size(), vts.size());
	auto te = decltype(vt)(1)[0];
	auto tse = decltype(vts)(1)[0];
	vector res(m, tuple_cat(te, tse));
	for (size_t i = 0; i < m; i++) res[i] = tuple_cat(vt[i], vts[i]);
	return res;
}

ll power(ll n, ll k) {
	ll res = 1;
	while (k) {
		if (k & 1) res *= n;
		n *= n;
		k >>= 1;
	}
	return res;
}

ll powerMod(ll n, ll k, ll mod) {
	ll res = 1;
	while (k) {
		if (k & 1) res = res * n % mod;
		n = n * n % mod;
		k >>= 1;
	}
	return res;
}

template<int mod>
struct ModInt {
	ll x;
	constexpr ModInt(ll a = 0) noexcept : x(a >= 0 ? a % mod : (a % mod + mod)) {};

	constexpr ModInt& operator+=(const ModInt& r) noexcept {
		x += r.x;
		if (x >= mod) x -= mod;
		return *this;
	}
	constexpr ModInt& operator-=(const ModInt& r) noexcept {
		x -= r.x;
		if (x < 0) x += mod;
		return *this;
	}
	constexpr ModInt& operator*=(const ModInt& r) noexcept {
		x = x * r.x % mod;
		return *this;
	}
	constexpr ModInt& operator/=(const ModInt& r) noexcept {
		return *this *= r.inverse();
	}

	constexpr ModInt operator+(const ModInt& r) const noexcept { return ModInt(*this) += r; }
	constexpr ModInt operator-(const ModInt& r) const noexcept { return ModInt(*this) -= r; }
	constexpr ModInt operator*(const ModInt& r) const noexcept { return ModInt(*this) *= r; }
	constexpr ModInt operator/(const ModInt& r) const noexcept { return ModInt(*this) /= r; }
	constexpr ModInt operator-() const noexcept { return ModInt(-x); };
	constexpr bool operator==(const ModInt& r) const noexcept { return x == r.x; }
	constexpr bool operator!=(const ModInt& r) const noexcept { return x != r.x; }
	constexpr ModInt& operator++() noexcept {
		(*this) += 1;
		return *this;
	}
	constexpr ModInt& operator--() noexcept {
		(*this) -= 1;
		return *this;
	}
	constexpr ModInt operator++(int) noexcept {
		ModInt tmp(*this);
		++(*this);
		return tmp;
	}
	constexpr ModInt operator--(int) noexcept {
		ModInt tmp(*this);
		--(*this);
		return tmp;
	}

	constexpr ModInt inverse() const noexcept {
		ll xx = 1, u = 0, s = x, t = mod;
		ll k;
		while (t) {
			k = s / t;
			swap(s -= k * t, t);
			swap(xx -= k * u, u);
		}
		return ModInt(xx);
	}

	constexpr ModInt power(ll k) const noexcept {
		ModInt res = 1, y = x;
		while (k) {
			if (k & 1) res *= y;
			y *= y;
			k >>= 1;
		}
		return res;
	}

	friend istream& operator>>(istream& is, ModInt& r) {
		ll s;
		is >> s;
		r = ModInt<mod>(s);
		return is;
	}

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

vector<vector<int>> graph(int n, int m, bool directed = 0, int origin = 1) {
	vector<vector<int>> g(n);
	while (m--) {
		int u, v;
		cin >> u >> v;
		u -= origin, v -= origin;
		g[u].emplace_back(v);
		if (!directed) g[v].emplace_back(u);
	}
	return g;
}

auto weightedGraph(int n, int m, bool directed = 0, int origin = 1) {
	struct Edge {
		int to; ll w;
		Edge(int to, ll w) : to(to), w(w) {}
	};
	vector<vector<Edge>> g(n);
	while (m--) {
		int u, v;
		ll w;
		cin >> u >> v >> w;
		u -= origin, v -= origin;
		g[u].emplace_back(Edge(v, w));
		if (!directed) g[v].emplace_back(Edge(u, w));
	}
	return g;
}

#define INCLUDED_MAIN
#include __FILE__
#endif

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