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.
'''input
1
733629261048200000 361714100

'''
from math import gcd

def solve():
    a, b = map(int, input().split())
    if a%b!=0:
        print(a)
    else:
        k = a//b
        i = 2
        mi = a
        while i*i<=b:
            if b%i == 0:
                while b%i == 0:
                    b//=i
                c = 0
                while k%i == 0:
                    k//=i
                    c+=1
                mi = min(mi, pow(i, c+1))
            i+=1
            #print(b)
        if b!=1:
            c = 0
            while k%b == 0:
                k//=b
                c+=1
                #print("-->", k, b)
            mi = min(mi, pow(b, c+1))
        print(a//mi)

def main():
    t = 1
    t = int(input())
    for _ in range(t):
        solve()
main()