zjuoj 3609 Modular Inverse

http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=3609

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

References

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

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

分析：
题目要求给出a和m的值 ， 求出 ax % m == 1 % m成立时的x 的最小值 ， 直接x枚举到m即可。

一开始写的时候没有想到是枚举到m， 后来队友推出m。

AC代码：

 #include<cstdio>
 #include<algorithm>
 #include<cstring>
 #include<queue>
 #include<iostream>
 #include<stack>
 #include<map>
 #include<string>
 using namespace std;
 int main(){
     int n, x, a, m;
     scanf("%d", &n);
     while(n--){
         bool flag = true;
         scanf("%d%d", &a, &m);
         for(x = ; x <= m; x++){
             if((a*x)%m == %m){
                 flag = false;
                 printf("%d\n", x);
                 break;
             }
         }
         if(flag){
             printf("Not Exist\n");
         }
     }
     return ;
 }