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 collections import Counter
import math
import sys
# A function to print all prime factors of
# a given number n
def primeFactors(n):
    a = []
    # Print the number of two's that divide n
    while n % 2 == 0:
        a.append(2)
        n //= 2

    # n must be odd at this point
    # so a skip of 2 ( i = i + 2) can be used
    for i in range(3, int(math.sqrt(n)) + 1, 2):
        # while i divides n , print i ad divide n
        while n % i == 0:
            a.append(i)
            n //= i
            # Condition if n is a prime
    # number greater than 2
    if n > 2:
        a.append(n)
    return Counter(a)

cases = int(input())
for t in range(cases):
    p,q = list(map(int,input().split()))
    if p%q!=0:
        print(p)
    else:
        qprime = primeFactors(q)
        pprime = {}
        for i in qprime:
            x = p
            c = 0
            while x%i==0:
                c+=1
                x//=i
            pprime[i]=c
        mv = pow(10,20)
        for i in qprime:
            v = pprime[i]-(qprime[i]-1)
            mv = min(mv,pow(i,v))
        output = p//mv
        print(output)
