Test/Combination.test.cpp

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Last update: 2021-06-05 13:56:14+09:00
Problem: https://yukicoder.me/problems/no/1181

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Code

#define PROBLEM "https://yukicoder.me/problems/no/1181"

#include "Mathematics/ModInt.hpp"
#include "Mathematics/Combination.hpp"

#include <cstdio>
#include <vector>

constexpr int MOD = 1000000007;
using mint = ModInt<MOD>;
Combination<mint> comb;
using ll = long long;

int main() {
	int N;
	ll K;
	scanf("%d %lld", &N, &K);
	K %= MOD;
	
	mint sum = mint(1 + K) * K / 2;
	std::vector<mint> powk(N + 1);
	powk[0] = 1;
	for (int i = 1; i < N; ++i) powk[i] = powk[i - 1] * K;
	mint ans = mint(K).pow(N), p = 1;
	for (int i = 0; i < N; ++i) {
		mint pat = comb(N, i) * powk[N - i];
		ans += pat * p;
		p *= sum;
	}
	printf("%d\n", ans.val());
}

#line 1 "Test/Combination.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1181"

#line 1 "Mathematics/ModInt.hpp"



#include <cassert>
#include <iostream>
#include <cstdint>

/**
 * @brief https://tkmst201.github.io/Library/Mathematics/ModInt.hpp
 */
template<int M>
struct ModInt {
	static_assert(M > 0);
	
	using value_type = int;
	using calc_type = std::int_fast64_t;
	
private:
	value_type val_;
	
public:
	constexpr ModInt(calc_type val = 0) : val_(val % M + (val >= 0 ? 0 : M)) {}
	constexpr value_type val() const noexcept { return val_; }
	constexpr static decltype(M) mod() noexcept { return M; }
	
	explicit constexpr operator bool() const noexcept { return val_; }
	constexpr bool operator !() const noexcept { return !static_cast<bool>(*this); }
	constexpr ModInt operator +() const noexcept { return *this; }
	constexpr ModInt operator -() const noexcept { return ModInt(val_ == 0 ? 0 : M - val_); }
	constexpr ModInt operator ++(int) noexcept { ModInt res = *this; ++*this; return res; }
	constexpr ModInt operator --(int) noexcept { ModInt res = *this; --*this; return res; }
	constexpr ModInt & operator ++() noexcept { val_ = val_ + 1 == M ? 0 : val_ + 1; return *this; }
	constexpr ModInt & operator --() noexcept { val_ = val_ == 0 ? M - 1 : val_ - 1; return *this; }
	constexpr ModInt & operator +=(const ModInt & rhs) noexcept { val_ += val_ < M - rhs.val_ ? rhs.val_ : rhs.val_ - M; return *this; }
	constexpr ModInt & operator -=(const ModInt & rhs) noexcept { val_ += val_ >= rhs.val_ ? -rhs.val_ : M - rhs.val_; return *this; }
	constexpr ModInt & operator *=(const ModInt & rhs) noexcept { val_ = static_cast<calc_type>(val_) * rhs.val_ % M; return *this; }
	constexpr ModInt & operator /=(const ModInt & rhs) noexcept { return *this *= rhs.inv(); }
	friend constexpr ModInt operator +(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) += rhs; }
	friend constexpr ModInt operator -(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) -= rhs; }
	friend constexpr ModInt operator *(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) *= rhs; }
	friend constexpr ModInt operator /(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) /= rhs; }
	friend constexpr bool operator ==(const ModInt & lhs, const ModInt & rhs) noexcept { return lhs.val_ == rhs.val_; }
	friend constexpr bool operator !=(const ModInt & lhs, const ModInt & rhs) noexcept { return !(lhs == rhs); }
	friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val_; }
	friend std::istream & operator >>(std::istream & is, ModInt & rhs) { calc_type x; is >> x; rhs = ModInt(x); return is; }
	
	constexpr ModInt pow(calc_type n) const noexcept {
		ModInt res = 1, x = val_;
		if (n < 0) { x = x.inv(); n = -n; }
		while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }
		return res;
	}
	
	constexpr ModInt inv() const noexcept {
		value_type a = val_, a1 = 1, b = M, b1 = 0;
		while (b > 0) {
			const value_type q = a / b;
			value_type tmp = a - q * b; a = b; b = tmp;
			tmp = a1 - q * b1; a1 = b1; b1 = tmp;
		}
		assert(a == 1);
		if (a1 < 0) a1 += M;
		return a1;
	}
};


#line 1 "Mathematics/Combination.hpp"



#include <vector>
#line 6 "Mathematics/Combination.hpp"
#include <algorithm>

/**
 * @brief https://tkmst201.github.io/Library/Mathematics/Combination.hpp
 */
template<typename T>
struct Combination {
	using size_type = std::size_t;
	
private:
	std::vector<T> fact_, finv_, inv_;
	static constexpr size_type MAX_LIMIT = 50000000;
	
public:
	explicit Combination(size_type sz = 1) : fact_(1, 1), finv_(1, 1), inv_(1, 1) { build(sz); }
	
	T fact(size_type k) { if (k >= T::mod()) return 0; build(k); return fact_[k]; }
	T finv(size_type k) { assert(k < T::mod()); build(k); return finv_[k]; }
	T inv(size_type k) { assert(k > 0 && k < T::mod()); build(k); return inv_[k]; }
	T operator ()(int n, int r) { return c(n, r); }
	T c(int n, int r) {
		if (r < 0 || n < r) return 0;
		return fact(n) * finv(r) * finv(n - r);
	}
	
private:
	void build(size_type k) {
		if (fact_.size() > k) return;
		assert(k < MAX_LIMIT);
		size_type sz = std::min({MAX_LIMIT, static_cast<size_type>(T::mod()), std::max(fact_.size() * 2, k + 1)});
		size_type presz = fact_.size();
		fact_.resize(sz);
		finv_.resize(sz);
		inv_.resize(sz);
		for (size_type i = presz; i < sz; ++i) fact_[i] = fact_[i - 1] * i;
		finv_[sz - 1] = fact_[sz - 1].inv();
		for (size_type i = sz - 1; i > presz; --i) {
			finv_[i - 1] = finv_[i] * i;
			inv_[i] = fact_[i - 1] * finv_[i];
		}
		inv_[presz] = fact_[presz - 1] * finv_[presz];
	}
};


#line 5 "Test/Combination.test.cpp"

#include <cstdio>
#line 8 "Test/Combination.test.cpp"

constexpr int MOD = 1000000007;
using mint = ModInt<MOD>;
Combination<mint> comb;
using ll = long long;

int main() {
	int N;
	ll K;
	scanf("%d %lld", &N, &K);
	K %= MOD;
	
	mint sum = mint(1 + K) * K / 2;
	std::vector<mint> powk(N + 1);
	powk[0] = 1;
	for (int i = 1; i < N; ++i) powk[i] = powk[i - 1] * K;
	mint ans = mint(K).pow(N), p = 1;
	for (int i = 0; i < N; ++i) {
		mint pat = comb(N, i) * powk[N - i];
		ans += pat * p;
		p *= sum;
	}
	printf("%d\n", ans.val());
}