中国剩余定理

Posted 2020-11-09 $mathcal{Lance1ot}$

233

RT

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstdlib>
#define inr long long
using namespace std;
inr exgcd(inr a,inr b,inr &x,inr &y)
{
    if(!b)
    {
        x=1;
        y=0;
        return 0;
    }
    exgcd(b,a%b,x,y);
    inr k=x;
    x=y;
    y=k-a/b*y;
    return 0;
}
inr a[21],b[21];
int main()
{
    inr n;
    cin>>n;
    inr M=1;
    for(int i=1;i<=n;i++)
    {
        cin>>a[i]>>b[i];
        M*=a[i];
    }
    inr ans=0;
    for(int i=1;i<=n;i++)
    {
        inr x,y;
        exgcd(M/a[i],a[i],x,y);
        ans=(ans+x*M/a[i]*b[i])%M;
    }
    cout<<(ans+M)%M;
}