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 math

def factorize(n):
	primes = {}

	for d in range(2, int(n ** 0.5) + 1):
		while n % d == 0:
			if d not in primes:
				primes[d] = 1
			else:
				primes[d] += 1
			n //= d 
		if n == 1:
			break
	if n != 1:
		primes[n] = 1

	return primes


################################### MAIN ################################### 

def main():
	t = int(input())

	for i in range(t):
		p, q = map(int, input().split())
		
		if p % q:
			print(p)
			continue

		q_primes = factorize(q)
		result = 1
		for prime in q_primes:
			temp = p
			while temp % prime == 0:
				temp //= prime

			x = temp * (prime ** (q_primes[prime] - 1))
			result = max(result, x)

		print(result)

if __name__ == '__main__':
	main()
