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.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class A {

    private static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    private static BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));
    private static StringTokenizer st;

    public static void main(String[] args) throws Exception {
        st = new StringTokenizer(reader.readLine());
        int T = Integer.parseInt(st.nextToken());
        for (int t = 0; t < T; t++) {
            st = new StringTokenizer(reader.readLine());
            long p = Long.parseLong(st.nextToken());
            long q = Long.parseLong(st.nextToken());
            long x;
            if (p % q != 0) {
                x = p;
            } else {
                Map<Long, Long> fq = factor(q);
                long smallest = Long.MAX_VALUE;
                for (Map.Entry<Long, Long> entry : fq.entrySet()) {
                    long f = entry.getKey();
                    long exponentInP = 0;
                    long pCopy = p;
                    while (pCopy % f == 0) {
                        exponentInP++;
                        pCopy /= f;
                    }
                    long diff = exponentInP - (entry.getValue() - 1);
                    long toDivide = power(f, diff);
                    smallest = Math.min(smallest, toDivide);
                }
                x = p / smallest;
            }
            writer.write(Long.toString(x));
            writer.newLine();
            writer.flush();
        }
    }

    public static Map<Long, Long> factor(long n) {
        Map<Long, Long> res = new HashMap<>();
        long d = 2;
        while (n > 1 && d * d <= n) {
            long counter = 0;
            while (n % d == 0) {
                counter++;
                n /= d;
            }
            if (counter > 0) {
                res.put(d, counter);
            }
            d++;
        }
        if (n > 1) {
            res.put(n, 1L);
        }
        return res;
    }

    public static long power(long x, long y) {
        long res = 1;
        while (y > 0) {
            if ((y & 1) != 0) {
                res = res * x;
            }
            y = y >> 1;
            x = x * x;
        }
        return res;
    }

}
