ZOJ 3609 Modular Inverse

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

33 114 125 13

Sample Output

4Not Exist8

References

• http://en.wikipedia.org/wiki/Modular_inverse

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Author: WU, Zejun
Contest: The 9th Zhejiang Provincial Collegiate Programming Contest

#include <iostream>

#include <cstdio>

#include <cstring>

using namespace std;

int main()

{

    int a,m;

    int T;

    cin>>T;

while(T--)

{

    cin>>a>>m; int i;

    for(i=1;i<=m;i++)

    {

        if((i*a-1)%m==0)

            break;

    }

    if(i==m+1)

        puts("Not Exist");

    else

        printf("%d\n",i);

}

    return 0;

}