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.
def count(n, p):
    r = 0
    while n % p == 0:
        n //= p
        r += 1
    return r


def candidate(p, q, d):
    ep = count(p, d)
    eq = count(q, d)
    assert ep >= eq
    return p // (d ** (ep - eq + 1))


def solve(p, q):
    if p % q > 0:
        return p
    res = -1
    d = 2
    while d * d <= q:
        if q % d == 0:
            cur = candidate(p, q, d)
            if cur > res:
                res = cur
            while q % d == 0:
                q //= d
        d += 1
    if q > 1:
        cur = candidate(p, q, q)
        if cur > res:
            res = cur
    assert p % res == 0
    assert res != -1
    return res


tc = int(input())
for _ in range(tc):
    p, q = map(int, input().split())
    print(solve(p, q))