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.util.*;
public class division {

	public static void main(String[] args) {

//		Scanner sc = new Scanner(System.in);
		FastReader sc = new FastReader();
		int t = sc.nextInt();
		for(int o = 0 ; o<t;o++) {
			long p = sc.nextLong();
			long q = sc.nextLong();
			long x = q;
			HashSet<Long> set = new HashSet<>();
			
			for(long i = 2; i*i<=x;i++) {
				
				while(x%i==0) {
					set.add(i);
					x = x/i;
				}
				
			}
			if(x>1) {
				set.add(x);
			}
			long ans = 0;
			for(long a : set) {
				long f = p;
				
				while(f % q ==0) {
					f = f/a;
				}
				if(f>ans) {
					ans = f;
				}
			}
		
		System.out.println(ans);
		}
	}
}
			
			
			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;
    }
}
