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 math


def getFactors(num):
    factors = {}
    for i in range(2, int(math.sqrt(num)) + 1):
        while num % i == 0:
            if i not in factors:
                factors[i] = 0
            factors[i] += 1
            num //= i
    if num >= 2:
        if num not in factors:
            factors[num] = 0
        factors[num] += 1
    return factors


def getGCD(a, b):
    while b != 0:
        a, b = b, a % b
    return a


def solve(p, q):
    gcd = getGCD(p, q)
    remain = p // gcd
    if gcd != q:
        return p
    gcdFact = getFactors(gcd)
    minDiv = math.inf
    for factor in gcdFact:
        r = remain
        rFact = 0
        while r % factor == 0:
            r //= factor
            rFact += 1
        div = factor ** (rFact + 1)
        minDiv = min(div, minDiv)
    return p // minDiv


if __name__ == "__main__":
    T = int(input())
    for _ in range(T):
        p, q = [int(x) for x in input().split()]
        print(solve(p, q))
