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.
INF = 10**20

def f(n):
    d = 2
    a = {}
    counter = {}
    x = n
    while d * d <= n:
        while x % d == 0:
            if d in a:
                a[d] += 1
                counter[d] *= d
            else:
                a[d] = 1
                counter[d] = d
            x //= d
        d += 1
    if x != 1:
        a[x] = 1
        counter[x] = x
    return (a, counter)
            

t = int(input())
for i in range(t):
    a, b = map(int, input().split())
    if a % b != 0:
        print(a)
    else:
        l, count = f(b)
        best = 2
        result = INF
        for key in l:
            num = 1
            while a % num == 0:
                num *= key
            k = num // count[key]
            if k < result:
                result = k
                best = key
        print(a // result)
            
            
            
    
