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.
def primeFactors(n):
    pn=n
    l={}
    while n % 2 == 0:
        if 2 not in l:
            l[2]=1
        else:
            l[2]+=1
        n = n // 2
    i=3
    while i*i<=n:
        while n % i== 0:
            if i not in l:
                l[i]=1
            else:
                l[i]+=1
            n = n // i
        i+=2
    if n > 2:
        l[n]=1
    # l[pn]=1
    return l
def solve(a,b):
    if a%b!=0:
        return a
    bp=primeFactors(b)
    ans=a
    for x in bp:
        powa=0
        oa=a
        while oa%x==0:
            oa//=x
            powa+=1
        dif=powa-bp[x]+1
        div=1
        for i in range(dif):
            div*=x
        ans=min(ans,div)
    return a//ans


for _ in range(int(input())):
    a,b=map(int,input().split())
    print(solve(a,b))


