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 defaultdict
primes = {i for i in range(2, 10**5)}
for i in range(2, 10**5):
    if i in primes:
        for j in range(2*i, 10**5, i):
            if j in primes:
                primes.remove(j)
primes = list(primes)
primes.sort()


def solve():
    p, q = map(int, input().split())
    P = p
    if p % q != 0:
        print(p)
        return
    #p%q == 0
    pdiv = defaultdict(int)
    qdiv = defaultdict(int)
    for i in range(2, q+1):
        if i*i > q:
            break
        if q % i == 0:
            while q % i == 0:
                pdiv[i] += 1
                qdiv[i] += 1
                p //= i
                q //= i
            while p % i == 0:
                pdiv[i] += 1
                p //= i
    if q > 1:
        qdiv[q] += 1
        while p % q == 0:
            pdiv[q] += 1
            p //= q
    ans = -1
    for v in pdiv.keys():
        ans = max(ans, P//(v**(pdiv[v] - qdiv[v] + 1)))
    print(ans)

    return


def main():
    testcase = int(input())
    for i in range(testcase):
        solve()
    return


if __name__ == "__main__":
    main()
