Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.

To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that: 

  * p_i is divisible by x_i; 
  * x_i is not divisible by q_i. 

Oleg is really good at division and managed to find all the answers quickly, how about you?

Input

The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.

Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.

Output

Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.

One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.

Example

Input


3
10 4
12 6
179 822


Output


10
4
179

Note

For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.

For the second pair, where p_2 = 12 and q_2 = 6, note that 

  * 12 is not a valid x_2, since 12 is divisible by q_2 = 6; 
  * 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6. 

The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
import java.util.*;

public class CodeForces1445C1{
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int t = input.nextInt();
		for(int j = 0;j<t;j++){
			long p = input.nextLong();
			int q = input.nextInt();
			long ans = 1;
			for(int i = 2;i*i<=q;i++){
				if(q%i == 0){
					ans = Math.max(ans,test(p,q,i));
					ans = Math.max(ans,test(p,q,q/i));
				}
			}

			if(p%q != 0){
				System.out.println(p);
			}
			else{
				System.out.println(Math.max(ans,test(p,q,q)));
			}
		}
	}


	public static long test(long p, long q, long t){
		long test = p;
		while(test%q == 0){
			test/= t;
		}

		return test;
	}
}