ZOJ 3609 Modular Inverse

Description

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 toax≡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
• 注意mod 1的逆元是1

  #include<iostream>
  #include<cstdio>
  #include<cstring>
  #include<cstdlib>
  #include<set>
  #include<ctime>
  #include<vector>
  #include<cmath>
  #include<algorithm>
  #include<map>
  #define ll long long
  using namespace std;
  const int maxn = 1e5 + 10;
  int T, n, m;
  
  void egcd(int a, int b, int &x, int &y)
  {
  	if (b == 0){ x = 1, y = 0; return; }
  	egcd(b, a % b, x, y);
  
  	long long t = x;
  	x = y, y = t - a / b * y;
  }
  
  int main()
  {
  	scanf("%d", &T);
  	while (T--)
  	{
  		scanf("%d%d", &n, &m);
  		if (m == 1)
  		{
  			printf("1\n");
  			continue;
  		}
  		int x, y;
  		egcd(n, m, x, y);
  		x = (x % m + m) % m;
  		if (n*x%m == 1)printf("%d\n", x);
  		else printf("Not Exist\n");
  	}
  	return 0;
  }