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.*;
import java.lang.*;

public class Rextester 
{
	static long p,q;
	static long ans;
	public static void f(long x)
	{
		long t=p;
		while(t%q==0) t/=x;
		ans=Math.max(ans,t);
	}
	public static void main(String[] args) 
	{
		Scanner sc=new Scanner (System.in);
		int T=sc.nextInt();
		while(T-->0)
		{
			p=sc.nextLong();
			q=sc.nextLong();
			if(p%q!=0) System.out.println(p);
			else
			{
				ans=1;
				long x=q;
				for(long i=2;i*i<=x;i++)
				{
					if(x%i==0) f(i); 
					while(x%i==0) x/=i;
				}
				if(x>1) f(x);
				System.out.println(ans);
			}
		}
	}
}