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 CF1444A{
  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());
        }
        
    } 
    
    static int MOD=998244353;
    static int[] rk, p,siz;
    public static void main(String[] args){
        FastReader br=new FastReader(); int T=br.nextInt();
        
        for (int j = 0; j < T; j++) {
            long A=br.nextLong(); int B=br.nextInt();
            if(A%B>0){
                System.out.println(A);continue;
            }
            //Prime factorize B
            ArrayList<Integer> p=new ArrayList<>();
            ArrayList<Integer> d=new ArrayList<>();
        
            int cnt=0; long Q=A/B;
            for (int i = 2; i <=Math.sqrt(B); i++) {
                cnt=1;
                if(B%i==0){
                    B/=i;
                    while(Q%i==0){
                        Q/=i; cnt++;
                    }
                    p.add(i); d.add(cnt);
                }
                while(B%i==0){B/=i;}
            }
            if(B>1){
                cnt=1;
                while(Q%B==0){
                        Q/=B; cnt++;
                }
                p.add(B); d.add(cnt);
            }
            long min=A;
            for(int i=0;i<p.size();i++){
                
                min=Math.min(min,pow(p.get(i),d.get(i)));
                
            }
            System.out.println(A/min);
        }
    }
    public static long pow(int b, int e){
        if(e==0)return 1; if(e==1)return b;
        long a=pow(b,e/2);
        return a*a*pow(b,e&1);
    }
    
    
}
//Debugging:
//Are you sure your algorithm is correct?
//Bounds: long
//Special cases: n=0,1?
//Make sure you remove your debugging code before you submit!