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.*;
import java.util.*;


public class Test2  {
	  static FastReader f = new FastReader();
	public static void main(String[] args) throws IOException {	
        int t = f.nextInt();
        while(t-->0) {
        	long p = f.nextLong();
        	int q = f.nextInt();
        	ArrayList<Integer> fec = primeFectors(q);
        	long ret = 1;
        	for(int e:fec) {
        		long temp = p;
        		while(temp%q==0)temp/=e;
        		
        		ret = Math.max(ret, temp);
        		
        	}
        	System.out.println(ret);
        }
    }
	static ArrayList<Integer> primeFectors(int n){
		ArrayList<Integer> ret = new ArrayList<Integer>();
		while (n%2==0)
        {
           ret.add(2);
            n /= 2;
        }
		for (int i = 3; i <= Math.ceil(Math.sqrt(n)); i+= 2)
        {
			
            // While i divides n, print i and divide n
            while (n%i==0)
            {
                ret.add(i);
                n /= i;
            }
        }
		 if (n > 2)
	            ret.add(n);
		return ret;
	}
	static class FastReader 
    { 
         BufferedReader br; 
        StringTokenizer st; 
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 	  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
}



