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
import math
input = sys.stdin.readline

############ ---- Input Functions ---- ############


def inp():
    return(int(input()))


def inlt():
    return(list(map(int, input().split())))


def insr():
    s = input()
    return(list(s[:len(s) - 1]))


def invr():
    return(map(int, input().split()))


t = inp()

for asdf in range(t):
    p, q = invr()

    prime = []

    if p % q != 0:
        print(p)
    else:
        tmpq = q
        for i in range(2, 1 + math.floor(math.sqrt(tmpq))):
            if q == 1:
                break
            if q % i == 0:
                q = q//i
                prime.append([i, 1])
            while(q % i == 0):
                q = q//i
                prime[-1][1] += 1
        if q != 1:
            prime.append([q, 1])
        # print(prime)
        result = 1
        for a in prime:
            tmpp = p
            pr = a[0]
            qex = a[1]
            pex = 0
            while(tmpp % pr == 0):
                tmpp = tmpp//pr
                pex += 1
            for j in range(qex-1):
                tmpp *= pr
            # print(pr, qex, tmpp)
            if result < tmpp:
                result = tmpp
        print(result)
