同余方程组

@(XSY)[中国剩余定理]
中国剩余定理.
注意求逆元要用exGCD.

#include <cstdio>
#include <cctype>

const int N = 8;

void exGCD(long long a, long long b, long long &x, long long &y)
{
	if(! b)
	{
		x = 1, y = 0;
		return;
	}
	
	exGCD(b, a % b, y, x);
	y -= a / b * x;
}

int main()
{
	#ifndef ONLINE_JUDGE
	freopen("CRT.in", "r", stdin);
	freopen("CRT.out", "w", stdout);
	#endif
	
	int n;
	scanf("%d", &n);
	static int b[N], m[N];
	long long prd = 1;
	
	for(int i = 0; i < n; ++ i)
		scanf("%d%d", b + i, m + i), prd *= m[i];
	
	long long ans = 0;
	
	for(int i = 0; i < n; ++ i)
	{
		long long x, y;
		exGCD(prd / m[i], m[i], x, y);
		ans += b[i] * (prd / m[i]) * ((x + m[i]) % m[i]);
	}
	
	printf("%lld", ans % prd);
}