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 f(a):
    A = {}

    def one_mnogetel(a):
        for i in range(2, int(a ** 0.5) + 1):
            if a % i == 0:
                return i
        return a

    while one_mnogetel(a) != a:
        g = one_mnogetel(a)
        if g in A:
            A[g] += 1
        else:
            A[g] = 1
        a = a // g
    if a in A:
        A[a] += 1
    else:
        A[a] = 1
    return A

x = int(input())
for _ in range(x):
    p, q = map(int, input().split())
    if p % q != 0:
        print(p)
    elif p == 1:
        print(1)
    elif q== p:
        z = True
        for i in range(2, int(q ** 0.5) + 1):
            if q % i == 0:
                print(q // i)
                z = False
                break
        if z:
            print(1)
    else:
        p0 = int(p)
        A = f(q)
        n = 10 ** 20
        for key in A:
            z = 0
            while p % key == 0:
                p //= key
                z += 1
            n = min(n, key ** (z - A[key] + 1))
        print(p0 // n)
