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 math import pow
 
 
def pizda(n):
   i = 2
   primfac = []
 
   while i * i <= n:
       while n % i == 0:
           primfac.append(i)
           n = n // i
       i = i + 1
   if n > 1:
       primfac.append(n)
   return primfac
 
 
 
t=int(input())
 
for j in range(t):
 
    p,q = map(int,input().split())
    if p%q!=0:
        print(p)
    else:
        a = pizda(q)
 
        b = []
        f = [a[0]]
        for i in range(1, len(a)):
            if a[i] == a[i - 1]:
                f.append(a[i])
            else:
                b.append(f)
                f = [a[i]]
 
        b.append(f)
 
        a = []
        c = []
        for i in range(len(b)):
            a.append(b[i][0])
            c.append(len(b[i]))
 
        b = [0 for i in range(len(a))]
        p1 = p
 
        for i in range(len(a)):
            while p % a[i] == 0:
                p = p // a[i]
                b[i] += 1
 
        for i in range(len(a)):
            b[i] = max(0, b[i] - c[i] + 1)
 
        for i in range(len(a)):
            b[i] = a[i]**b[i]
 
        b.sort()
        print(p1 // b[0])