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.
from math import gcd
def facts(n):
    ans = []
    while n%2 == 0:
        ans.append(2)
        n = n//2
    for i in range(3, int(n**0.5+7), 2):
        while n%i == 0:
            ans.append(i)
            n = n // i
    if n > 2:
        ans.append(n)
    ans.sort()
    return ans
t = int(input())
for _ in range(t):
    p, q = [int(p) for p in input().split()]
    if p < q:
        print(p)
        continue
    elif p == q:
        ok = False
        if q%2 == 0:
            print(p//2)
            continue
        else:
            for i in range(3, int(q**0.5)+1, 2):
                if q%i == 0:
                    ok = True
                    print(max(q//i, i))
                    break
        if not ok:
            print(1)
    elif p%q != 0:
        print(p)
        continue
    elif p%q == 0:
        f1 = facts(q)
        t = p//q
        ans = 1
        for i in range(len(f1)):
            ele = p
            while ele%f1[i] == 0:
                ele = ele // f1[i]
                if ele%q:
                    ans = max(ans, ele)
                    break
        print(ans)
