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 sqrt

def pr(p):
    if p<=3:
        return [[p,1]]
    i=2
    n=int(sqrt(p))+1
    res=[]
    while i<n:
        if p%i==0:
            res.append([i,0])
            while p%i==0:
                p=p//i
                res[-1][1]+=1
        i+=1
    if p>1:
        res.append([p,1])
    return res

def kkk(x,p):
    res=0
    while x%p==0:
        x=x//p
        res+=1
    return res

for _ in range(int(input())):
    p,q=map(int,input().split())
    pp=pr(q)
    ans=1
    for x in pp:
        a=x[0]
        k=x[1]
        h=kkk(p,a)
        temp=p
        if h<k: ans=p
        else:
            for j in range(h-k+1):
                temp=temp//a
            ans=max(ans,temp)
    print(ans)
                
        
    
