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.*;

import static java.lang.Math.*;

public class Main {
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);
        int t = nextInt();
        for (int g = 0; g < t; g++) {
            long p = nextLong();
            long q = nextInt();
            if (q > p || p % q != 0) pw.println(p);
            else {
                ArrayList<Long> del = new ArrayList<>();
                for (long i = 2; i * i <= q; i++) {
                    if (q % i == 0) {
                        long sec = q / i;
                        del.add(sec);
                        del.add(i);
                    }
                }
                del.add(q);
                long max = 0;
                if ((p / q) % q != 0) max = p / q;
                for (Long l : del) {
                    long p1 = p;
                    while (p % q == 0) {
                        p /= l;
                    }
                    max = max(p, max);
                    p = p1;
                }
                pw.println(max);
            }
        }
        pw.close();
    }

    static ArrayList<Pair>[] g;

    static PrintWriter pw;
    static StringTokenizer st = new StringTokenizer("");
    static BufferedReader br;

    static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}

class Pair {
    int del;
    int pow;

    public Pair(int del, int pow) {
        this.del = del;
        this.pow = pow;
    }
}
