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.
'''Author- Akshit Monga'''
from sys import stdin,stdout
input=stdin.readline
import math

def printDivisors(n,q):
    i = 1
    ans=-1
    while i <= math.sqrt(q):
        if (n % i == 0):
            if n/i==i and i%q!=0:
                ans=max(ans,i)
            else:
                if i%q!=0:
                    ans=max(ans,i)
                if (n//i)%q!=0:
                    ans=max(ans,(n//i))
        i = i + 1
    print(ans)


def primeFactors(n):
    arr=set()
    while n % 2 == 0:
        arr.add(2)
        n = n // 2
    for i in range(3, int(math.sqrt(n)) + 1, 2):
        while n % i == 0:
            arr.add(i)
            n = n // i
    if n > 2:
        arr.add(n)
    return arr

t = int(input())
for _ in range(t):
    p,q=map(int,input().split())
    if p<q:
        print(p)
    else:
        if p%q!=0:
            print(p)
        else:
            q1=q
            q2=p//q
            arr=list(primeFactors(q1))
            ans=-1
            for i in arr:
                val1=q1//i
                val2=q2
                while val2 % i == 0:
                    val2=val2//i
                ans=max(ans,val1*val2)
            # print(ans)
            stdout.write(str(ans)+'\n')
            # print(int(ans))