#423975 (C++14) No.980 Fibonacci Convolution Hard

• 問題: No.980 Fibonacci Convolution Hard
• ユーザー: square1001
• 提出日時: 2020-01-31 22:18:46
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 446 ms / 2,000 ms
• コード長: 2,835 bytes
• コンパイル時間: 663 ms
• コンパイル使用メモリ: 68,320 KB
• 実行使用メモリ: 6,816 KB
• 最終ジャッジ日時: 2024-09-17 11:32:12
• 合計ジャッジ時間: 10,402 ms
• ジャッジサーバーID （参考情報）: judge3 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	446 ms; 6,816 KB
testcase_01	AC	425 ms; 5,376 KB
testcase_02	AC	416 ms; 5,376 KB
testcase_03	AC	420 ms; 5,376 KB
testcase_04	AC	427 ms; 5,376 KB
testcase_05	AC	410 ms; 5,376 KB
testcase_06	AC	416 ms; 5,376 KB
testcase_07	AC	404 ms; 5,376 KB
testcase_08	AC	417 ms; 5,376 KB
testcase_09	AC	432 ms; 5,376 KB
testcase_10	AC	433 ms; 5,376 KB
testcase_11	AC	421 ms; 5,376 KB
testcase_12	AC	434 ms; 5,376 KB
testcase_13	AC	411 ms; 5,376 KB
testcase_14	AC	430 ms; 5,376 KB
testcase_15	AC	396 ms; 5,376 KB
testcase_16	AC	381 ms; 5,376 KB

ソースコード

#ifndef CLASS_MODINT
#define CLASS_MODINT

#include <cstdint>

template <std::uint32_t mod>
class modint {
private:
	std::uint32_t n;
public:
	modint() : n(0) {};
	modint(std::int64_t n_) : n((n_ >= 0 ? n_ : mod - (-n_) % mod) % mod) {};
	static constexpr std::uint32_t get_mod() { return mod; }
	std::uint32_t get() const { return n; }
	bool operator==(const modint& m) const { return n == m.n; }
	bool operator!=(const modint& m) const { return n != m.n; }
	modint& operator+=(const modint& m) { n += m.n; n = (n < mod ? n : n - mod); return *this; }
	modint& operator-=(const modint& m) { n += mod - m.n; n = (n < mod ? n : n - mod); return *this; }
	modint& operator*=(const modint& m) { n = std::uint64_t(n) * m.n % mod; return *this; }
	modint operator+(const modint& m) const { return modint(*this) += m; }
	modint operator-(const modint& m) const { return modint(*this) -= m; }
	modint operator*(const modint& m) const { return modint(*this) *= m; }
	modint inv() const { return (*this).pow(mod - 2); }
	modint pow(std::uint64_t b) const {
		modint ans = 1, m = modint(*this);
		while (b) {
			if (b & 1) ans *= m;
			m *= m;
			b >>= 1;
		}
		return ans;
	}
};

#endif // CLASS_MODINT

#include <iostream>
using namespace std;
using mint = modint<1000000007>;
pair<mint, mint> mul(pair<mint, mint> v1, pair<mint, mint> v2, mint d) {
	return make_pair(v1.first * v2.first + v1.second * v2.second * d, v1.second * v2.first + v1.first * v2.second);
}
pair<mint, mint> pow(pair<mint, mint> v, mint d, long long n) {
	pair<mint, mint> ans = make_pair(mint(1), mint(0));
	while (n > 0) {
		if (n & 1) ans = mul(ans, v, d);
		v = mul(v, v, d);
		n >>= 1;
	}
	return ans;
}
int main() {
	int P, Q;
	cin >> P >> Q;
	mint d = mint(P) * mint(P) + mint(4);
	mint dinv = d.inv();
	pair<mint, mint> alpha = make_pair(mint(2).inv() * mint(P), mint(2).inv());
	pair<mint, mint> beta = make_pair(mint(2).inv() * mint(P), mint(-2).inv());
	pair<mint, mint> diff = make_pair(alpha.first - beta.first, alpha.second - beta.second);
	mint g = diff.first * diff.first - diff.second * diff.second * d;
	pair<mint, mint> coeff = make_pair(diff.first * g.inv(), mint(-1) * diff.second * g.inv());
	coeff.first *= 2; coeff.second *= 2;
	for (int i = 0; i < Q; ++i) {
		long long X;
		cin >> X; X -= 2;
		pair<mint, mint> palpha = pow(alpha, d, X);
		pair<mint, mint> pbeta = pow(beta, d, X);
		pair<mint, mint> plus = make_pair((palpha.first + pbeta.first) * (X + 1), (palpha.second + pbeta.second) * (X + 1));
		palpha = mul(palpha, alpha, d);
		pbeta = mul(pbeta, beta, d);
		pair<mint, mint> minus = make_pair(palpha.first - pbeta.first, palpha.second - pbeta.second);
		minus = mul(minus, coeff, d);
		pair<mint, mint> ans = make_pair(plus.first - minus.first, plus.second - minus.second);
		cout << (ans.first * dinv).get() << '\n';
	}
	return 0;
}