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 Division {
    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int test = fs.nextInt();
        for (int t = 0; t < test; t++) {
            long p = fs.nextLong();
            long q = fs.nextLong();
            if (p % q != 0)
                out.println(p);
            else {
                long ans = 0;
                List<Long> primeDivisor = divisor(q);
                for (int i = 0; i < primeDivisor.size(); i += 2) {
                    long value = primeDivisor.get(i);
                    long power = primeDivisor.get(i + 1);
                    long currentValue = p / (long) Math.pow(value, power);
                    while (currentValue % value == 0) {
                        currentValue /= value;
                    }
                    ans = Math.max(ans, currentValue * (long) Math.pow(value, power - 1));
                }
                out.println(ans);
            }
        }
        out.println();
        out.close();
    }

    static long pow(long value, long power) {
        if (power == 1)
            return value;
        else if (power % 2 == 0)
            return pow(value, power / 2) * pow(value, power / 2);
        else
            return pow(value, power / 2) * pow(value, power / 2) * value;
    }

    static List<Long> divisor(long q) {
        List<Long> primeDivisor = new ArrayList<>();
        long count = 0;
        while (q % 2 == 0) {
            q /= 2;
            count++;
        }
        if (count > 0) {
            primeDivisor.add((long) 2);
            primeDivisor.add(count);
        }
        for (int i = 3; i * i <= q; i += 2) {
            count = 0;
            while (q % i == 0) {
                q /= i;
                count++;
            }
            if (count > 0) {
                primeDivisor.add((long) i);
                primeDivisor.add(count);
            }
        }
        if (q > 2) {
            primeDivisor.add(q);
            primeDivisor.add((long) 1);
        }
        return primeDivisor;
    }

    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++)
            a[i] = l.get(i);
    }

    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());
        }
    }

}