P4777 【模板】扩展中国剩余定理（EXCRT）&& Strange Way to Express Integers

 https://cn.vjudge.net/problem/POJ-2891  (换多组输入~)

https://www.luogu.org/problemnew/show/P4777

 

#include<algorithm>
#include<set>
#include<vector>
#include<queue>
#include<cmath>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<set>
#include<vector>
#include<queue>
#include<cmath>
#include<cstring>
#include<sstream>
#include<cstdio>
#include<ctime>
#include<map>
#include<stack>
#include<string>
using namespace std;

#define sfi(i) scanf("%d",&i)
#define pri(i) printf("%d\n",i)
#define sff(i) scanf("%lf",&i)
#define ll long long
#define mem(x,y) memset(x,y,sizeof(x))
#define INF 0x3f3f3f3f
#define eps 1e-6
#define PI acos(-1)
#define lowbit(x) ((x)&(-x))
#define zero(x) (((x)>0?(x):-(x))<eps)
#define fl() printf("flag\n")
#define MOD(x) ((x%mod)+mod)%mod
#define FASTIO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
ll gcd(ll a,ll b){while(b^=a^=b^=a%=b);return a;}
const int maxn=2e5+9;
const int mod=1e8+7;

inline ll read()
{
    ll f=1,x=0;
    char ss=getchar();
    while(ss<'0'||ss>'9'){if(ss=='-')f=-1;ss=getchar();}
    while(ss>='0'&&ss<='9'){x=x*10+ss-'0';ss=getchar();}
    return f*x;
}

//扩展欧几里得算法
void exgcd(ll a,ll b,ll &d,ll &x,ll &y)
{
    if(b==0){
        d=a;
        x=1,y=0;
    }
    else{
        exgcd(b,a%b,d,y,x);
        y-=(a/b)*x;
    }
}

//快速乘
ll qmul(ll a,ll b,ll M)
{
    ll ans=0;
    while(b>0)
    {
        if(b&1) ans=(ans+a)%M;
        a=(a+a)%M;
        b>>=1;
    }
    return ans;
}
//中国剩余定理
ll China(int n,ll *m,ll *a)
{
    ll M=m[0],d=0,y=0,x=0;
    ll ans=a[0];
    for(int i=1;i<n;i++)
    {
        ll aa=M;
        ll bb=m[i];
        ll cc=(a[i]-ans%bb+bb)%bb;//ax=c(mod b)

        ll g;
        exgcd(aa,bb,g,x,y);
        ll bnx=bb/g;
        if(cc%g!=0) return -1;
        x=qmul(x,cc/g,bnx);
        ans=ans+x*M;
        M*=bnx;
        ans=(ans%M+M)%M;
    }
    return (ans%M+M)%M;
}
ll m[maxn],a[maxn];
int main()
{
    //FASTIO;
    //#define endl '\n'
    int n;
    scanf("%d",&n);
    for(int i=0;i<n;i++)
        scanf("%lld%lld",&m[i],&a[i]);
    printf("%lld",China(n,m,a));
}