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 rc{
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t--!=0){
		    long p=sc.nextLong(),q=sc.nextLong(),x=1;
		    List<Long> list = new ArrayList<>();
		    if(p%q!=0)
		       System.out.println(p);
		    else{
		        factors(q,list);
		        //System.out.println(list);
		        for(long i:list){
		           long a=p; 
		           while(a%i==0){
		              a/=i;
		              if(a%q!=0){
		                 x=Math.max(x,a);
		                 break;
		              }    
		           }
		        }
		        System.out.println(x);
		    }    
		}
	}
	static List<Long> factors(long q, List<Long> list){
	    list.add(q);
	    for(long i=2; i*i<=q; i++){
	        if(q%i==0){
	             list.add(i); 
	             if(i!=q/i)
	                list.add(q/i);
	        }
	    }
	    return list;
	}
}