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 array import array  # noqa: F401
from typing import List, Tuple, TypeVar, Generic, Sequence, Union  # noqa: F401


def input():
    return sys.stdin.buffer.readline().decode('utf-8')


def get_primes(n: int):
    from itertools import chain
    from array import array
    primes = [2, 3]
    is_prime = (array('b', (0, 0, 1, 1, 0, 1, 0)) +
                array('b', (1, 0, 0, 0, 1, 0)) * ((n - 1) // 6))

    for i in chain.from_iterable((range(5, n + 1, 6), range(7, n + 1, 6))):
        if is_prime[i]:
            primes.append(i)
            for j in range(i * 3, n + 1, i * 2):
                is_prime[j] = 0

    return is_prime, primes


def main():
    t = int(input())
    _, primes = get_primes(50000)

    for _ in range(t):
        pi, qi = map(int, input().split())
        if pi % qi:
            print(pi)
            continue

        ans = 1
        for p in primes:
            if qi % p == 0:
                cnt = 0
                while qi % p == 0:
                    cnt += 1
                    qi //= p
                x = pi
                while x % p == 0:
                    x //= p
                ans = max(ans, x * (p**(cnt - 1)))
        if qi > 1 and pi % qi == 0:
            while pi % qi == 0:
                pi //= qi
            ans = max(ans, pi)
        print(ans)


if __name__ == '__main__':
    main()
