Strange Way to Express Integers扩展欧几里德

#include <iostream>
#include<stdio.h>
#include<string.h>
#include<queue>
#include <math.h>
#include<string.h>
#include <algorithm>
#define INF 1000000000
using namespace std;
//typedef long long LL;
long long ggcd(long long a,long long b,long long&x,long long&y)
{
    long long d,t;
    if(b==0)
    {
        x=1;
        y=0;
        return a;
    }
    d=ggcd(b,a%b,x,y);
    t=x-a/b*y;
    x=y;
    y=t;
     return d;

}
int main()
{
    long long  a1,r1,a2,r2,a,b,c,x0,y0,m,t;
    int i,n;
    while(scanf("%d",&n)!=EOF)
    {
        int bj=1;
        scanf("%lld%lld",&a1,&r1);
        for(i=1;i<n;i++)
        {
            scanf("%lld%lld",&a2,&r2);
            a=a1;
            b=a2;
            c=r2-r1;
            m=ggcd(a,b,x0,y0);
            if(c%m)
                bj=0;
            t=b/m;
            x0*=(c/m);
            x0=(x0%t+t)%t;
            r1=a1*x0+r1;
            a1=a1*(a2/m);

        }
        if(bj==0)
        {
            printf("-1\n");
        }
        else
            printf("%lld\n",r1);
    }
    return 0;
}

Elina is reading a book written by Rujia Liu, which introduces a strange way to express non-negative integers. The way is described as following:

Choose k different positive integers a₁, a₂, …, a_k. For some non-negative m, divide it by every a_i (1 ≤ i ≤ k) to find the remainder r_i. If a₁, a₂, …, a_k are properly chosen, m can be determined, then the pairs (a_i, r_i) can be used to express m.

“It is easy to calculate the pairs from m, ” said Elina. “But how can I find m from the pairs?”

Since Elina is new to programming, this problem is too difficult for her. Can you help her?

Input

The input contains multiple test cases. Each test cases consists of some lines.

• Line 1: Contains the integer k.
• Lines 2 ~ k + 1: Each contains a pair of integers a_i, r_i (1 ≤ i ≤ k).

Output

Output the non-negative integer m on a separate line for each test case. If there are multiple possible values, output the smallest one. If there are no possible values, output -1.

Sample Input

2
8 7
11 9

Sample Output

31

从后往前推有一个固定的式子；x=1;y=0；....

x=y;y=x-a/b*y;