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 sys import stdin

tt = int(stdin.readline())

for loop in range(tt):

    p,q = map(int,stdin.readline().split())

    if p % q != 0:
        print (p)
        continue

    bk = {}
    for i in range(2,10**5):
        if q % i == 0:
            bk[i] = 0
            while q % i == 0:
                bk[i] += 1
                q //= i
        if bk == 1:
            break

    if q != 1:
        bk[q] = 1

    #print (bk)

    ans = float("-inf")
    for i in bk:
        cnt = 0
        tp = p
        while tp % i == 0:
            tp //= i
            cnt += 1
        ans = max(ans , p // (i**(cnt-bk[i]+1)))

    print (ans)