UVA - 11388 GCD LCM

UVA - 11388 GCD LCM

II U C ONLINE C ON TEST 2 008

Problem D: GCD LCM

Input: standard input
Output: standard output

The GCD of two positive integers is the largest integer that divides both the integers without any remainder. The LCM of two positive integers is the smallest positive integer that is divisible by both the integers. A positive integer can be the GCD of many pairs of numbers. Similarly, it can be the LCM of many pairs of numbers. In this problem, you will be given two positive integers. You have to output a pair of numbers whose GCD is the first number and LCM is the second number.

Input

The first line of input will consist of a positive integer T. T denotes the number of cases. Each of the next T lines will contain two positive integer, G and L.

Output

For each case of input, there will be one line of output. It will contain two positive integers a and b, a ≤ b, which has a GCD of G and LCM of L. In case there is more than one pair satisfying the condition, output the pair for which a is minimized. In case there is no such pair, output -1.

Constraints

- T ≤ 100

- Both G and L will be less than 2³¹.

Sample Input

Output for Sample Input

2

1 2

3 4

1 2

-1

Problem setter: Shamim Hafiz

題意： 給你兩個數的gcd和lcm，讓你求時候是唯一的一對n，m，輸出最小的一對

思路：設n = a*b*c*d, m = a*b*c*e, 那麼gcd=a*b*c, lcm = a*b*c*d*e,那麼如果不是唯一的話，那麼lcm%gcd != 0,因為d和e的位置可以排列，要唯一的話，一定是lcm是gcd的倍數，且這對就是最小的

#include 
#include 
#include 
#include 
typedef long long ll;
using namespace std;

int main() {
	int t, n, m;
	scanf("%d", &t);
	while (t--) {
		scanf("%d%d", &n, &m);
		if (m % n == 0)
			printf("%d %d\n", n, m);
		else printf("-1\n");
	}
	return 0;
}