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 math import gcd as _gcd


def main():
    t = int(input())
    for i_t in range(t):
        p, q = _read_ints()
        if p % q != 0:
            x = p
        else:
            q_factors = _represent_as_prime_factors(q)
            x = max(
                p // q_factor**_count_factor(p, q_factor)
                * q_factor**(q_factor_n-1)
                for q_factor, q_factor_n in q_factors.items()
            )
        print(x)


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


def _represent_as_prime_factors(x):
    if x < 1 or x != int(x):
        raise ValueError("can't represent as prime factors")
    x = int(x)
    
    result = dict()
    
    potential_factor = 2
    while potential_factor ** 2 <= x:
        if x % potential_factor == 0:
            result[potential_factor] = _count_factor(x, potential_factor)
            x //= potential_factor**result[potential_factor]
        potential_factor += 1
    
    if x != 1:
        result[x] = 1
    
    return result


def _count_factor(x, factor):
    result = 0
    while x % factor == 0:
        x //= factor
        result += 1
    return result


if __name__ == "__main__":
    main()
