結果

問題 No.891 隣接3項間の漸化式
コンテスト
ユーザー polylogK
提出日時 2019-09-21 15:33:43
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 6,663 bytes
コンパイル時間 2,015 ms
コンパイル使用メモリ 175,584 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-18 23:55:45
合計ジャッジ時間 3,264 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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 * 3
other AC * 39
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 # 

#include <bits/stdc++.h>
using namespace std::literals::string_literals;
using i64 = long long;
using std::cout;
using std::endl;
using std::cin;

template<typename T>
std::vector<T> make_v(size_t a){return std::vector<T>(a);}

template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts){
  return std::vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}

template <std::uint_fast64_t Modulus>
class modint {
	using u32 = std::uint_fast32_t;
	using u64 = std::uint_fast64_t;
	using i64 = std::int_fast64_t;
	
	public:
	u64 a;

	constexpr modint() noexcept : a(0) {}
	constexpr modint(const u64 & x) noexcept : a(x % Modulus) {}

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

	const modint inverse() const {
		i64 x = a, b = Modulus, u = 1, v = 0;
		while(b > 0) {
			auto t = x / b;

			std::swap(x -= t * b, b);
			std::swap(u -= t * v, v);
		}
		return modint(u);
	}
	const modint pow(i64 k) const {
		return modint(*this) ^ k;
	}

	static u64 mod() { return Modulus; }

	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);
	}
	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 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; };
	explicit operator bool() const { return a; }
	explicit operator u32() const { 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;
	}
};

template<class T>
class square_matrix {
	using value_type = T;
	using i64 = int64_t;
	
	std::vector<std::vector<value_type>> data;

	public:
	square_matrix() {}
	square_matrix(const size_t & n) : data(n, std::vector<value_type>(n, T())) {}
	
	static const square_matrix E(const size_t & n) {
		square_matrix e(n);
		for(size_t i = 0; i < n; i++) e[i][i] = 1;
		return e;
	}
	static const square_matrix O(const size_t & n) {
		return square_matrix(n);
	}
	
	const size_t height() const {
		return data.size();
	}
	const size_t width() const {
		return data.size();
	}
	const T determinant() const {
		square_matrix B(*this);
		T ret = 1;
		for(int i = 0; i < width(); i++) {
			int ind = -1;
			for(int j = i; j < width(); j++) {
				if(B[j][i] == 0) continue;
				ind = j;
			}
			if(ind == -1) return 0;
			if(i != ind) {
				ret *= -1;
				std::swap(B[i], B[ind]);
			}

			ret *= B[i][i];
			for(int j = 0; j < width(); j++) B[i][j] /= B[i][i];
			for(int j = i + 1; j < width(); j++)
				for(int k = 0; k < width(); k++)
					B[j][k] -= B[i][k] * B[j][i];
		}
		return ret;
	}
	
	const std::vector<value_type> & operator[](const size_t & k) const {
		return data.at(k);
	}
	std::vector<value_type> & operator[](const size_t & k) {
		return data.at(k);
	}
	square_matrix & operator+=(const square_matrix & B) {
		assert(height() == B.height());
		for(int i = 0; i < height(); i++)
			for(int j = 0; j < width(); j++)
				(*this)[i][j] += B[i][j];
		return (*this);
	}
	square_matrix & operator-=(const square_matrix & B) {
		assert(height() == B.height());
		for(int i = 0; i < height(); i++)
			for(int j = 0; j < width(); j++)
				(*this)[i][j] -= B[i][j];
		return (*this);
	}
	square_matrix & operator*=(const square_matrix & B) {
		assert(height() == B.height());
		auto C = square_matrix::O(height());
		for(int i = 0; i < height(); i++)
			for(int j = 0; j < width(); j++)
				for(int k = 0; k < height(); k++)
					C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
		return (*this) = C;
	}
	square_matrix & operator^=(i64 k) {
		auto B = square_matrix::E(height());
		while(k) {
			if(k & 1) B *= (*this);
			(*this) *= (*this);
			k >>= 1;
		}
		return (*this) = B;
	}
	square_matrix & operator=(const square_matrix & B) {
		(*this).data = B.data;
		return (*this);
	}
	const square_matrix operator+(const square_matrix & B) const {
		return (square_matrix(*this) += B);
	}
	const square_matrix operator-(const square_matrix & B) const {
		return (square_matrix(*this) -= B);
	}
	const square_matrix operator*(const square_matrix & B) const {
		return (square_matrix(*this) *= B);
	}
	const square_matrix operator^(const i64 & k) const {
		return (square_matrix(*this) ^= k);
	}
	const bool operator==(const square_matrix & B) const {
		return (data == B.data);
	}
	friend std::ostream & operator<<(std::ostream & os, square_matrix & p) {
		for(int i = 0; i < height(); i++) {
			os << "[";
			for(int j = 0; j < width(); j++) {
				os << p[i][j] << (j + 1 == width() ? "]\n" : ", ");
			}
		}
		return os;
	}
};

using mint = modint<(int)(1e9 + 7)>;

int main() {
	int a, b, n; scanf("%d%d%d", &a, &b, &n);
	if(n == 0) {
		printf("0\n");
		return 0;
	}

	square_matrix<mint> A(2);
	A[0][0] = a;
	A[0][1] = b;
	A[1][0] = 1;
	A ^= n - 1;
	
	printf("%d\n", A[0][0]);
	return 0;
}
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