Test/garner.test.cpp

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Last update: 2021-06-05 13:56:14+09:00
Problem: https://yukicoder.me/problems/no/187

Depends on

Code

#define PROBLEM "https://yukicoder.me/problems/no/187"

#include "Mathematics/garner.hpp"

#include <cstdio>
#include <vector>

int main() {
	int N;
	scanf("%d", &N);
	std::vector<int> b(N), m(N);
	bool zero = true;
	for (int i = 0; i < N; ++i) scanf("%d %d", &b[i], &m[i]), zero &= b[i] == 0;
	
	constexpr int mod = 1000000007;
	if (!tk::pre_garner(b, m)) puts("-1");
	else if (zero) {
		long long ans = 1;
		for (auto c : m) ans = ans * c % mod;
		printf("%lld\n", ans);
	}
	else printf("%d\n", tk::garner<int, long long>(b, m, mod));
}

#line 1 "Test/garner.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/187"

#line 1 "Mathematics/garner.hpp"



#include <vector>
#include <cassert>
#include <type_traits>

#line 1 "Mathematics/euclid.hpp"



#line 5 "Mathematics/euclid.hpp"
#include <utility>
#include <tuple>
#line 8 "Mathematics/euclid.hpp"
#include <cmath>

/**
 * @brief https://tkmst201.github.io/Library/Mathematics/euclid.hpp
 */
namespace tk {
template<typename T>
constexpr T gcd(T a, T b) noexcept {
	static_assert(std::is_integral<T>::value);
	assert(a >= 0);
	assert(b >= 0);
	while (b != 0) {
		const T t = a % b;
		a = b; b = t;
	}
	return a;
}

template<typename T>
constexpr T lcm(T a, T b) noexcept {
	static_assert(std::is_integral<T>::value);
	assert(a >= 0);
	assert(b >= 0);
	if (a == 0 || b == 0) return 0;
	return a / gcd(a, b) * b;
}

template<typename T>
constexpr std::tuple<T, T, T> ext_gcd(T a, T b) noexcept {
	static_assert(std::is_integral<T>::value);
	static_assert(std::is_signed<T>::value);
	assert(a != 0);
	assert(b != 0);
	T a1 = (a > 0) * 2 - 1, a2 = 0, b1 = 0, b2 = (b > 0) * 2 - 1;
	a = std::abs(a);
	b = std::abs(b);
	while (b > 0) {
		const T q = a / b;
		T tmp = a - q * b; a = b; b = tmp;
		tmp = a1 - q * b1; a1 = b1; b1 = tmp;
		tmp = a2 - q * b2; a2 = b2; b2 = tmp;
	}
	return {a, a1, a2};
}
} // namespace tk



#line 1 "Mathematics/mod_pow_inv.hpp"



#line 6 "Mathematics/mod_pow_inv.hpp"

/**
 * @brief https://tkmst201.github.io/Library/Mathematics/mod_pow_inv.hpp
 */
namespace tk {
template<typename T>
constexpr T mod_pow(T x, T n, T m) noexcept {
	static_assert(std::is_integral<T>::value);
	assert(m > 0);
	assert(n >= 0);
	x = x % m + (x >= 0 ? 0 : m);
	T res = 1 % m;
	while (n > 0) {
		if (n & 1) res = res * x % m;
		x = x * x % m;
		n >>= 1;
	}
	return res;
}

template<typename T>
constexpr T mod_inv(T x, T m) noexcept {
	static_assert(std::is_integral<T>::value);
	static_assert(std::is_signed<T>::value);
	assert(m > 0);
	x = x % m + (x >= 0 ? 0 : m);
	T x1 = 1, y = m, y1 = 0;
	while (y > 0) {
		const T q = x / y;
		T tmp = x - q * y; x = y; y = tmp;
		tmp = x1 - q * y1; x1 = y1; y1 = tmp;
	}
	assert(x == 1);
	if (x1 == m) x1 = 0;
	if (x1 < 0) x1 += m;
	return x1;
}
} // namespace tk



#line 10 "Mathematics/garner.hpp"

/**
 * @brief https://tkmst201.github.io/Library/Mathematics/garner.hpp
 */
namespace tk {
template<typename T>
bool pre_garner(std::vector<T> & b, std::vector<T> & m) noexcept {
	static_assert(std::is_integral<T>::value);
	static_assert(std::is_signed<T>::value);
	for (int i = 0; i < static_cast<int>(b.size()); ++i) {
		b[i] = b[i] % m[i] + (b[i] >= 0 ? 0 : m[i]);
		for (int j = 0; j < i; ++j) {
			T g = gcd(m[i], m[j]);
			if ((b[i] - b[j]) % g != 0) return false;
			m[i] /= g; m[j] /= g;
			T gi = gcd(g, m[i]), gj = g / gi;
			do {
				g = gcd(gi, gj);
				gi *= g; gj /= g;
			} while (g != 1);
			m[i] *= gi; m[j] *= gj;
			b[i] %= m[i]; b[j] %= m[j];
		}
	}
	return true;
}

template<typename T, typename U>
T garner(const std::vector<T> & b, const std::vector<T> & m, const T M) {
	static_assert(std::is_integral<T>::value);
	assert(b.size() == m.size());
	const int n = b.size();
	assert(n > 0);
	{
		T g = 0;
		for (auto v : m) {
			assert(v > 0);
			g = gcd(g, v);
		}
		assert(n == 1 || g == 1);
	}
	assert(M > 0);
	std::vector<T> sum(n + 1, 0), ip(n + 1, 1);
	for (int i = 0; i < n; ++i) {
		if (m[i] == 1) continue;
		U t = (b[i] % m[i] + static_cast<U>(2) * m[i] - sum[i]) % m[i] * mod_inv(ip[i], m[i]) % m[i];
		for (int j = i + 1; j < n; ++j) {
			sum[j] = (sum[j] + ip[j] * t) % m[j];
			ip[j] = static_cast<U>(ip[j]) * m[i] % m[j];
		}
		sum[n] = (sum[n] + ip[n] * t % M) % M;
		ip[n] = static_cast<U>(ip[n]) * m[i] % M; 
	}
	return sum.back();
}
} // namespace tk



#line 4 "Test/garner.test.cpp"

#include <cstdio>
#line 7 "Test/garner.test.cpp"

int main() {
	int N;
	scanf("%d", &N);
	std::vector<int> b(N), m(N);
	bool zero = true;
	for (int i = 0; i < N; ++i) scanf("%d %d", &b[i], &m[i]), zero &= b[i] == 0;
	
	constexpr int mod = 1000000007;
	if (!tk::pre_garner(b, m)) puts("-1");
	else if (zero) {
		long long ans = 1;
		for (auto c : m) ans = ans * c % mod;
		printf("%lld\n", ans);
	}
	else printf("%d\n", tk::garner<int, long long>(b, m, mod));
}