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.
primes = []
preprocessing = [1]*pow(10,5)
preprocessing[0] = 0
preprocessing[1] = 0
preprocessing[2] = 1

ind = 2
while ind < len(preprocessing):
    if preprocessing[ind]:
        primes.append(ind)
        k = 2
        while ind*k < len(preprocessing):
            preprocessing[ind*k] = 0
            k += 1
    ind += 1

T = int(input())

for t in range(T):
    p,q = [int(k) for k in input().split()]

    qq = q

    factors = []

    for prime in primes:
        if qq % prime == 0:
            while qq % prime == 0:
                qq //= prime
            factors.append(prime)

    largest = 0

    for f in factors:
        x = p
        if (p % x == 0) and (x % q != 0):
            largest = x
        while x % f == 0:
            x //= f
            if (p % x == 0) and (x % q != 0):
                largest = max(x,largest)

    tmp = q
    for f in factors:
        while tmp % f == 0:
            tmp //= f

    if tmp > 1:
        f = tmp
        x = p
        if (p % x == 0) and (x % q != 0):
            largest = x
        while x % f == 0:
            x //= f
            tmp //= f
            if (p % x == 0) and (x % q != 0):
                largest = max(x,largest)
    print(largest)
