【模板】扩展中国剩余定理（EXCRT）

一、题目：

洛谷模板

二、代码：

#include<iostream>
#include<cstdio>
#include<cstring>

#define LL long long
#define mem(s,v) memset(s,v,sizeof(s))
#define FILE(s) freopen(s".in","r",stdin);freopen(s".out","w",stdout)

using namespace std;
template<class Type>
inline Type read(Type num){
    Type x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return f*x;
}

const int maxn=100005;

int n;
LL ai[maxn],bi[maxn];

inline LL mult(LL a,LL b,LL p){
    LL ret=0;
    for(;b;b>>=1){
        if(b&1)ret=(ret+a)%p;
        a=(a+a)%p;
    }
    return ret;
}

inline LL exgcd(LL a,LL b,LL &x,LL &y){
    if(b==0){x=1;y=0;return a;}
    LL d=exgcd(b,a%b,x,y);
    LL z=x;x=y;y=z-a/b*y;
    return d;
}

inline LL excrt(void){
    LL x,y;
    LL M=bi[1],ans=ai[1];
    for(register int i=2;i<=n;++i){
        LL a=M,b=bi[i],c=(ai[i]-ans%b+b)%b;
        LL gcd=exgcd(a,b,x,y),bg=b/gcd;
        if(c%gcd!=0)return -1;

        x=mult(x,c/gcd,bg);
        ans+=x*M;
        M*=bg;
        ans=(ans%M+M)%M;
    }
    return (ans%M+M)%M;
}

int main(){
    n=read(n);
    for(register int i=1;i<=n;++i){
        bi[i]=read(bi[i]);
        ai[i]=read(ai[i]);
    }
    printf("%lld
",excrt());
    return 0;
}