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.
	// _________________________RATHOD_____________________________________________________________
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;  
public class Main 
{ 
    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; 
        } 
    }
    public static void main(String[] args) 
    { 
       FastReader sc=new FastReader(); 
       //Scanner sc=new Scanner(System.in);
        int t;
        t=1;
        t=sc.nextInt();
       // StringBuilder sb=new StringBuilder();
        while(t>0)
        {
            t--;
            long p=sc.nextLong();
            long q=sc.nextLong();
            if(p<q)
            System.out.println(p);
            else if(p%q!=0)
            System.out.println(p);
            else
            {
               // int f=1;
                ArrayList<Long> arl=new ArrayList<Long>();
                long i=1;
                for(i=1;i<=Math.sqrt(q);i++)
                {
                    if(q%i==0)
                    {
                    arl.add(i);
                    arl.add(q/i);
                    }
                }
                Collections.sort(arl);
                //long tem=p;
                long sol=Long.MIN_VALUE;
                for(int j=1;j<arl.size();j++)
                {
                    long temp=p;
                    long fact=arl.get(j);
                    while(temp%fact==0&&temp%q==0)
                    temp=temp/fact;
                    sol=Math.max(sol,temp);
                    //System.out.println(sol+" "+fact);
                }
                System.out.println(sol);
                
            }
            
            
        }
    }
}