ZOJ 3609Modular 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

33 114 125 13

Sample Output

4Not Exist8

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 longusing 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;}