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.
'''input
3
10 4
78 13
179 822
'''
from sys import stdin,stdout
I = lambda : map(int,stdin.readline().split())
import bisect
import math
from heapq import heappop, heappush
from collections import defaultdict, deque
# t = 1
import math  
def testcase():
	a,b = I()
	div = []
	def getDivisors(n) : 
		i = 1
		while i <= math.sqrt(n): 
			if (n % i == 0) : 
				if ((n / i) == i) : 
					div.append(i) 
				else : 
					div.append(i) 
					div.append(n/i) 
			i = i + 1
	if a%b == 0:
		getDivisors(b)
		div.sort()
		div = div[1:]
		tmp = a
		ans = 1
		for i in div:
			a = tmp
			while a%i == 0:
				# print a,i
				if (a/i)%b != 0:
					ans = max(ans,a/i)
				a/=i
		print ans
	else:
		print a
t = input() 
for i in range(t):
	testcase()
	