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 sys
input=sys.stdin.readline
from collections import *
import math
def prime(q,al):
    t=q
   
    for i in range(2,int(math.sqrt(t))+1):

        while(q%i==0):
            al[i]+=1
            q=q//i

    if(q>1):
        al[q]+=1
    q=t
    return;

def power(p,x):
    t1=p
    cnt=0
    while(p%x==0):
        p=p//x
        cnt+=1
    p=t1
    return cnt;
        


a=int(input())
for x in range(a):
    p,q=map(int,input().split())

    al=defaultdict(int)

    prime(q,al)

    new=defaultdict(int)
    for i in al:
        new[i]=al[i]

    
    for i in new:
        y=power(p,i)
        new[i]=y
    
    flag=0
    for i in al:
        if(al[i]>new[i]):
            flag=1
            break;
    
    if(flag==0):
        number=-1


        powers=-1
        val=math.inf
        for i in al:
            reduc=new[i]-(al[i]-1)

            v1=pow(i,reduc)
            if(v1<val):
                powers=al[i]-1
                number=i
                val=v1
        
        new[number]=powers
       

    for i in new:
        alpha=power(p,i)
        p=p//pow(i,alpha-new[i])
    print(p)
    
