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.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Division {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while (t-- > 0) {
			long p = sc.nextLong();
			long q = sc.nextLong();
			if (p % q != 0) {
				System.out.println(p);
			} else {
				System.out.println(divisor(p, q));
			}
		}
	}
	
	private static long divisor(long p, long q) {
        List<Long> primes = getPrimes(q);
        long ans = 0;
        for (long fact : primes) {
        	long x = p;
        	while (x % q == 0) {
				x /= fact;
			}
        	ans = Math.max(ans, x);
		}
        return ans;
    }

	private static List<Long> getPrimes(long n) {
		// TODO Auto-generated method stub
		List<Long> primes = new ArrayList<Long>();
		while (n % 2 == 0) {
			primes.add((long) 2);
			n /= 2;
		}
		for (long i = 3; i <= Math.sqrt(n); i+=2) {
			while (n % i == 0) {
				primes.add(i);
				n /= i;
			}
		}
		if (n > 2) {
			primes.add(n);
		}
		return primes;
	}

}
