Modular Inverse(扩展欧几里得)

Modular Inverse

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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The modular modular multiplicative inverse of an integer a modulo m is an integer x such that a-1≡x (mod m). This is equivalent to ax≡1 (mod m).

Input

There are multiple test cases. The first line of input is an integer T ≈ 2000 indicating the number of test cases.

Each test case contains two integers 0 < a ≤ 1000 and 0 < m ≤ 1000.

Output

For each test case, output the smallest positive x. If such x doesn't exist, output "Not Exist".

Sample Input

3
3 11
4 12
5 13

Sample Output

4
Not Exist
8

#include <iostream>
#include <cstring>
#include <algorithm>
#include <map>
using namespace std;

typedef long long ll;

int t;
int a,b,X,Y;

int gdc(int a,int b){
    return b==0?a:gdc(b,a%b);
}

void exgdc(int a,int b,int &X,int &Y){
    if(b==0){
        X=1;
        Y=0;
        return;
    }
    exgdc(b,a%b,X,Y);
    int temp=X;
    X=Y;
    Y=temp-a/b*Y;
}


int main(){
    ios::sync_with_stdio(false);
    while(cin>>t){
        while(t--){
            cin>>a>>b;
            int GDC=gdc(a,b);
            if(1%GDC!=0) {cout << "Not Exist" << endl;continue;}
            exgdc(a,b,X,Y);
            int res=X*(1/GDC);
            int ans=b/GDC;
            if(ans<0) ans=-ans;
            res%=ans;
            if(res<=0) res+=ans;   //题目说的是正数
            cout << res << endl;
        }
    }
    return 0;
}