結果

問題 No.1321 塗るめた
コンテスト
ユーザー polylogK
提出日時 2020-12-19 00:15:01
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 18 ms / 2,000 ms
コード長 4,362 bytes
コンパイル時間 2,070 ms
コンパイル使用メモリ 102,208 KB
最終ジャッジ日時 2025-01-17 03:09:55
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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 * 2
other AC * 45
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 # 

#line 1 "main.cpp"
#include <stdio.h>
#include <vector>

#line 1 "/home/ecasdqina/cpcpp/libs/library_cpp/math/modint.hpp"



#include <iostream>

namespace cplib {
template <std::uint_fast64_t Modulus>
class modint {
	using u32 = std::uint_fast32_t;
	using u64 = std::uint_fast64_t;
	using i32 = std::int_fast32_t;
	using i64 = std::int_fast64_t;

	inline u64 apply(i64 x) { return (x < 0 ? x + Modulus : x); };

public:
	u64 a;
	static constexpr u64 mod = Modulus;

	constexpr modint(const i64& x = 0) noexcept: a(apply(x % (i64)Modulus)) {}

	constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; }
	constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; }
	constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; }
	constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; }
	constexpr modint operator^(const u64& k) const noexcept { return modint(*this) ^= k; }
	constexpr modint operator^(const modint& k) const noexcept { return modint(*this) ^= k.value(); }
	constexpr modint operator-() const noexcept { return modint(Modulus - a); }
	constexpr modint operator++() noexcept { return (*this) = modint(*this) + 1; }
	constexpr modint operator--() noexcept { return (*this) = modint(*this) - 1; }
	const bool operator==(const modint& rhs) const noexcept { return a == rhs.a; };
	const bool operator!=(const modint& rhs) const noexcept { return a != rhs.a; };
	const bool operator<=(const modint& rhs) const noexcept { return a <= rhs.a; };
	const bool operator>=(const modint& rhs) const noexcept { return a >= rhs.a; };
	const bool operator<(const modint& rhs) const noexcept { return a < rhs.a; };
	const bool operator>(const modint& rhs) const noexcept { return a > rhs.a; };
	constexpr modint& operator+=(const modint& rhs) noexcept {
		a += rhs.a;
		if (a >= Modulus) a -= Modulus;
		return *this;
	}
	constexpr modint& operator-=(const modint& rhs) noexcept {
		if (a < rhs.a) a += Modulus;
		a -= rhs.a;
		return *this;
	}
	constexpr modint& operator*=(const modint& rhs) noexcept {
		a = a * rhs.a % Modulus;
		return *this;
	}
	constexpr modint& operator/=(modint rhs) noexcept {
		u64 exp = Modulus - 2;
		while (exp) {
			if (exp % 2) (*this) *= rhs;

			rhs *= rhs;
			exp /= 2;
		}
		return *this;
	}
	constexpr modint& operator^=(u64 k) noexcept {
		auto b = modint(1);
		while(k) {
			if(k & 1) b = b * (*this);
			(*this) *= (*this);
			k >>= 1;
		}
		return (*this) = b;
	}
	constexpr modint& operator=(const modint& rhs) noexcept {
		a = rhs.a;
		return (*this);
	}

	const modint inverse() const {
		return modint(1) / *this;
	}
	const modint power(i64 k) const {
		if(k < 0) return modint(*this).inverse() ^ (-k);
		return modint(*this) ^ k;
	}

	explicit operator bool() const { return a; }
	explicit operator u64() const { return a; }
	constexpr u64& value() noexcept { return a; }
	constexpr const u64& value() const noexcept { return a; }

	friend std::ostream& operator<<(std::ostream& os, const modint& p) {
		return os << p.a;
	}
	friend std::istream& operator>>(std::istream& is, modint& p) {
		u64 t;
		is >> t;
		p = modint(t);
		return is;
	}
};
}


#line 5 "main.cpp"
using mint = cplib::modint<998244353>;

int main() {
	int n, m, k; scanf("%d%d%d", &n, &m, &k);

	std::vector<mint> fact(n + 1, 1), factinv(n + 1, 1);
	for(int i = 0; i < n; i++) fact[i + 1] = fact[i] * (i + 1);
	factinv[n] = fact[n].inverse();
	for(int i = n - 1; i > 0; i--) factinv[i] = factinv[i + 1] * (i + 1);
	auto comb = [&](int n, int r) { return fact[n] * factinv[r] * factinv[n - r] ;};

    std::vector<int> prime, mip(m + k + 1); mip[0] = mip[1] = -1;
    for(int i = 2; i < mip.size(); i++) {
        if(mip[i] == 0) {
            mip[i] = i;
            prime.push_back(i);
        }

        for(int j = 0; j < prime.size() and prime[j] <= mip[i] and i * prime[j] < mip.size(); j++) {
            mip[i * prime[j]] = prime[j];
        }
    }

	std::vector<mint> pow(m + k + 1); pow[1] = 1;
	for(auto p: prime) pow[p] = mint(p).power(n);
	for(int i = 4; i < pow.size(); i++) pow[i] = pow[i / mip[i]] * pow[mip[i]];

	mint ans = 0;
	for(int i = 0; i <= k; i++) ans += comb(k, i) * pow[k + m - i] / fact[n] * (i % 2 ? -1 : 1);
	printf("%lld\n", (comb(m, k) * fact[n] * ans).value());
	return 0;
}
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