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.math.*;
import java.util.*;


// @author : Dinosparton 

public class test {
	 
	   static class Pair{ 
		   long x;
		   long y;
		   
		   Pair(long x,long y){ 
			   this.x = x;
			   this.y = y;
			   
		   }
	   }
	  
	   static class Compare { 
		   
		     void compare(Pair arr[], int n) 
		    { 
		        // Comparator to sort the pair according to second element 
		        Arrays.sort(arr, new Comparator<Pair>() { 
		            @Override public int compare(Pair p1, Pair p2) 
		            { 
		            	if(p1.x!=p2.x) {
		                return (int)(p1.x - p2.x); 
		            	}
		            	else { 
		            		return (int)(p1.y - p2.y);
		            	}
		            } 
		        }); 
		  
//		        for (int i = 0; i < n; i++) { 
//		            System.out.print(arr[i].x + " " + arr[i].y + " "); 
//		        } 
//		        System.out.println(); 
		    } 
		} 
	 
	   static class Scanner {
	        BufferedReader br;
	        StringTokenizer st;
	 
	        public Scanner()
	        {
	            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[]) throws Exception { 
		
		   
		   Scanner sc = new Scanner();
		   StringBuilder res = new StringBuilder();
		   
		   int tc = sc.nextInt();
		   
		   while(tc-->0) { 
			
			    long p = sc.nextLong();
			    long q = sc.nextLong();
			    
			    if(p%q!=0) { 
			    	res.append(p+"\n");
			    	continue;
			    }
			   
			    long ans=0;
			    
				 for(long i=2;i*i<=q;i++) {
					 
					 long temp=1;
					 while(q%i==0) {
						 temp*=i;
						 q/=i;
					 }
					 
					 long dup = p;
					 
					 while(dup %temp==0&&temp!=1)
						 dup /=i;
					 if(ans<dup &&temp!=1) {
						 ans=dup ;
						 }
				 }
				 long dup=p;
				 
				 while(dup%q==0&&q!=1)
					 dup/=q;
				 if(ans<dup&&q!=1) {
					 ans=dup;
					 }
				 res.append(ans+"\n");
		   }
		   
		   System.out.println(res);
	   }
}  




