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
from math import *
from fractions import *

def main():
    #n = int(sys.stdin.readline().strip())
    p, q = map(int, sys.stdin.readline().split())
    #q = list(map(int, sys.stdin.readline().split()))
    if p % q:
        print(p)
    else:
        res = 1
        i = 1
        while i * i <= q:
            if q % i == 0:
                a, s, d, f = p, q, 0, 0
                if i != 1:
                    while a % i == 0:
                        a //= i
                        d += 1
                    while s % i == 0:
                        f += 1
                        s //= i
                    a = p
                    while d >= f:
                        d -= 1
                        a //= i
                    res = max(res, a)
                a, s, d, f = p, q, 0, 0
                if q // i != 1:
                    g = q // i
                    while a % g == 0:
                        a //= g
                        d += 1
                    while s % g == 0:
                        f += 1
                        s //= g
                    a = p
                    while d >= f:
                        d -= 1
                        a //= g
                    res = max(res, a)  
            i += 1
                    
                    
                    
        print(res)
    
    
    
        
for i in range(int(input()) - 1): 
    main()
main()
    