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.
"""
Code of Ayush Tiwari
Codeforces: servermonk
Codechef: ayush572000

"""
import sys
input = sys.stdin.buffer.readline    

def solution():
    
    # This is the main code
    p,q=map(int,input().split())
    if p%q!=0:
        print(p)
    else:
        l=[]
        for i in range(2,int(q**0.5)+1):
            if q%i==0:
                l.append(i)
                if i!=q//i:
                    l.append(q//i)
        l.append(q)
        # print(l)
        ans=1
        for x in l:
            z=p
            while z%x==0:
                # print(z,x)
                z//=x
                if z%q!=0:
                    ans=max(ans,z)
                    break
        print(ans)
                
t=int(input())
for _ in range(t):
    solution()