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 __future__ import division,print_function
from heapq import*
import sys

le = sys.__stdin__.read().split("\n")[::-1]
af = []
def gc(a,b):
    while b:
        a,b=b,a%b
    return a
def f(p,q):
    d = 2
    m = 1
    r = q
    while d**2<=q:
        if q%d==0:
            a=p
            while a%q==0:
                a//=d
            while r%d==0:
                r//=d
            m=max(m,a)
        d+=1
    a=p
    if r!=1:
        while a%q==0:
            a//=r
        m=max(m,a)
    return m
for k in range(int(le.pop())):
    p,q = list(map(int,le.pop().split()))
    if p%q:
        af.append(p)
    else:
        af.append(f(p,q))
print("\n".join(map(str,af)))
