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 sqrt
def div(n):
    l=[]
    for i in range(2,int(sqrt(n))+3):
        if n%i==0:
            l.append(i)
        while n%i==0:
            n=n//i
    if n>1:
        l.append(n)
    return l



t=int(input())
for i in range(t):
   
    a=input()
    A=a.split()
    for i in range(2):
        A[i]=int(A[i])
    if A[0]%A[1]!=0:
        print(A[0])
    else:
        ss=div(A[1])
        max=1
        for i in ss:
            s=A[0]
            while s%A[1]==0:
                
                
                if s%i==0:
                    s=s//i
                
            if s>max:
                max=s
                    
        print(max)
         
                
                
            
        
        
            
        
    

    
    