ZOJ 3609 Modular Inverse

ZOJ Problem Set - 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 (modm). This is equivalent to ax≡1 (modm).

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

#include <cstdio>

int exgcd(int a, int b, int &x, int &y) {
	if (b == 0) {
		x = 1;
		y = 0;
		return a;
	}
	
	int gcd = exgcd(b, a % b, x, y);
	int tmp = x;
	x = y;
	y = tmp - a / b * y;
	return gcd;
}

int main() {
	int T;
	int a, b, x, y;

	scanf("%d", &T);

	while (T--) {
		scanf("%d%d", &a, &b);

		int gcd = exgcd(a, b, x, y);

		if (gcd != 1)
			puts("Not Exist");
		else {
			x = (x % b + b) % b;
			if (x == 0)
				x = 1;
			printf("%d\n", x);
		}
	}

	return 0;
}