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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

public class randoms {
    
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
     
        int T = Integer.parseInt(br.readLine());
        for(int t = 0; t < T; t++){
            StringTokenizer st = new StringTokenizer(br.readLine());
            long a = Long.parseLong(st.nextToken());
            long b = Long.parseLong(st.nextToken());
            if(a%b != 0){
                pw.println(a); continue;
            }
            long temp = a;
            long min = Long.MAX_VALUE;
            for(int i = 2; i*i <= b; i++)
            {
                if(b%i != 0) continue;
                long cur = 1;
                while(a%i == 0){
                    cur *= i;
                    a /= i;
                    if(b%i == 0){
                        cur /= i;
                        b /= i;
                    }
                }
                min = Math.min(min, cur*i);
            }
            long c = 1;
            if(a%b != 0) System.out.println("NAINSDFHWIRKLKLKKKLKLLKLKUHSDLFKSHDFLKWJFHDSL");
            while(b != 1 && a%b == 0){
                a /= b;
                c *= b;
            }
            if(c != 1) min = Math.min(min, c);
            pw.println(temp/min);
        }
        
        pw.close();
        br.close();
    }
}
/*
857754240051582063 933416507
*/