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
for i in range(int(input())):
 p,q=map(int,input().split())
 l=p
 if p%q!=0:
  print(p)
 else:
  g=[]
  c=1
  if q%2==0:
   while q%2==0:
    q=q//2
    p=p//2
   while p%2==0:
    c=c*2
    p=p//2
   g.append(c*2)
  for j in range(3,int(math.sqrt(q))+2,2):
   if q%j==0:
    c=1
    while q%j==0:
     q=q//j
     p=p//j
    while p%j==0:
     c=c*j
     p=p//j
    g.append(c*j)
  if q>2:
   c=1
   while p%q==0:
    c=c*q
    p=p//q
   g.append(c)
  print(l//(min(g)))