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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;

/**
 * @author Andrei Chugunov
 */
public class Main {

    private static class Solution {
        private void solve(FastScanner in, PrintWriter out) {
            int t = in.nextInt();

            for (int i = 0; i < t; i++) {
                long p = in.nextLong();
                long q = in.nextLong();
                long x = 0;

                if (p%q != 0) {
                    x = p;
                } else {
                    List<Long> factors = factorize(q);

                    x = 1;
                    for (long val : factors) {
                        long tmp = p;
                        while (tmp%val == 0) {
                            tmp = tmp/val;
                            if (tmp%q != 0) {
                                x = Math.max(x, tmp);
                                break;
                            }
                        }
                    }
                }

                out.println(x);
            }
        }

        List<Long> factorize(long x) {
            List<Long> factors = new ArrayList<>();

            for (long i = 2; i <= Math.sqrt(x); i++) {
                while (x % i == 0) {
                    factors.add(i);
                    x /= i;
                }
            }

            if (x != 1) {
                factors.add(x);
            }

            return factors;
        }
    }

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solution solver = new Solution();
        solver.solve(in, out);
        out.flush();
        //out.close();
    }

    private static class ArrayUtils {
        private static final long seed = System.nanoTime();
        private static final Random rand = new Random(seed);

        private static void sort(int[] a) {
            shuffle(a);
            Arrays.sort(a);
        }

        private static void shuffle(int[] a) {
            for (int i = 0; i < a.length; i++) {
                int j = rand.nextInt(i + 1);
                int t = a[i];
                a[i] = a[j];
                a[j] = t;
            }
        }

    }

    private static class FastScanner {
        private BufferedReader br;
        private StringTokenizer st;

        FastScanner(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream), 32768);
            st = null;
        }

        private String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        private int nextInt() {
            return Integer.parseInt(next());
        }

        private long nextLong() {
            return Long.parseLong(next());
        }

        private int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
    }
}
