拓展中国剩余定理（ex_crt）

#include <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <queue>
#include <stack>
#define ll long long
using namespace std;
ll n;
ll a[100005];
ll b[100005];
ll pow_add(ll x,ll y,ll mod)
{
    ll ans=0;
    while(y)
    {
        if(y%2)
        {
            ans+=x;
            ans%=mod;
        }
        y/=2;
        x+=x;
        x%=mod;
    }
    return ans;
}
ll gcd(ll x,ll y)
{
    if(y==0)
    {
        return x;
    }
    return gcd(y,x%y);
}
void ex_gcd(ll a,ll b,ll &x,ll &y)
{
    if(b==0)
    {
        x=1;
        y=0;
        return;
    }
    ex_gcd(b,a%b,x,y);
    ll t=x;
    x=y;
    y=t-(a/b)*x;
}
ll ex_crt()
{
    ll M0=a[1];
    ll ans=b[1];
    for(int i=2;i<=n;i++)
    {
        ll r=gcd(M0,a[i]);
        ll bb=((b[i]-ans)%a[i]+a[i])%a[i];
        if(bb%r)
        {
            return -1;
        }
        bb/=r;
        ll M=M0/r;
        ll aa=a[i]/r;
        ll x,y;
        ex_gcd(M,aa,x,y);
        x=pow_add(x,bb,aa);
        ans+=x*M0;
        M0*=aa;
        ans=(ans%M0+M0)%M0;
    }
    return (ans%M0+M0)%M0;
}
int main()
{
    scanf("%lld",&n);
    for(int i=1;i<=n;i++)
    {
        scanf("%lld%lld",&a[i],&b[i]);
    }
    printf("%lld\n",ex_crt());
    return 0;
}