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 defaultdict as dd, deque as dq,Counter as c
from math import factorial as f ,ceil,gcd,sqrt
for _ in range(int(input())):
	a,b = map(int,input().split())
	d = dd(lambda :0)
	p = dd(lambda :0)
	ans =float("inf")
	if a%b!=0:
		print(a)
	else:
		co =0
		while b%2==0:
			d[2]+=1
			b//=2
		temp = b
		for i in range(3,int(sqrt(temp))+1,2):
			if b%i==0:
				co =0
				while b%i==0:
					d[i]+=1
					b//=i
		if b>2:
			d[b]=1
		# print(d)
		temp =a 
		for i in d:
			while temp%i==0:
				p[i]+=1
				temp//=i
			ans = min(ans,i**(p[i]-d[i]+1))
			# print(ans)
		print(a//ans)