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.
from collections import Counter
def prime_dict(num):
	ans = Counter()
	while num % 2 == 0:
		num //= 2
		ans[2] += 1		
	for i in range(3, int(num ** 0.5) + 1, 2):
		while num % i == 0:
			num //= i
			ans[i] += 1
		if num == 1:
			break
	if num > 2:
		ans[num] += 1		
	return ans
def get_pow(a, b):
	ans = 0
	while a % b == 0:
		ans += 1
		a //= b
	return ans
t = int(input())
for _ in range(t):
	p, q = map(int, input().split())
	if p % q != 0:
		print(p)
	else:
		d = prime_dict(q)
		ans = 1
		for i in d:
			alp = get_pow(p, i)
			bet = d[i]
			ans = max(ans, p // (i ** (alp - bet + 1)))
		print(ans)