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
from sys import *
for _ in range(int(input())):
    n,m=map(int,iter(stdin.readline().split()))
    M,D=[],{}
    ans=n
    ord=n
    for i in range(2,int(math.sqrt(m))+1):
        if m%i==0:
            while(m%i==0):
                if i in D: D[i]+=1
                else: D[i]=1
                m//=i
    if m!=1:
        D.update({m:1})
    for key,values in D.items():
        count=0
        while(n%key==0):
            n//=key
            count+=1
        req=max(count-values+1,-999999999)
        val=1
        for i in range(0,req):
            val*=key
        ans=min(ans,val)
    stdout.write(str(ord//ans)+"\n")