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 C {
    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int T = 0;
        if(type == 0) T = fs.nextInt();
        else if(type == 1) T = 1;
        for(int t=0;t<T;t++) algo(fs);
    }

    static int type = 0; // 0 - known tcs, 1 - only 1 tcs

    public static void algo(FastScanner fs) {
        long p = fs.nextLong();
        long q = fs.nextLong();
        long min = Long.MAX_VALUE;
        ArrayList<Integer> P = primes(q);
        for(int prime : P) {
            int a = power(p, prime);
            int b = power(q, prime);
            if(b>a) {
                System.out.println(p);
                return;
            }
            else {
                long div = 1;
                for(int i=0;i<a-b+1;i++) div *= prime;
                min = Math.min(min, div);
            }
        }
        System.out.println(p/min);
    }

    static ArrayList<Integer> primes(long a) {
        ArrayList<Integer> p = new ArrayList<>();
        if(a%2 == 0) {
            p.add(2);
            while(a%2 == 0) a /= 2;
        }
        for(int i=3;i*i<=a;i+=2) {
            if(a%i == 0) {
                p.add(i);
                while(a%i == 0) a /= i;
            }
        }
        if(a > 2) p.add((int)a);
        //System.out.println("----");
        //for(int prime : p) System.out.print(prime + " ");
        //System.out.println();
        return p;
    }

    static int power(long a, long x) {
        int ans = 0;
        while(a%x == 0) {
            a /= x;
            ans++;
        }
        return ans;
    }



    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }
}
