1444_A. Division
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.
```python
from sys import stdin, stdout
from math import sqrt
#stdin = open('Q3.txt', 'r') 
def II(): return int(stdin.readline())
def MI(): return map(int, stdin.readline().split())
bigp=10**18+7

primes=[]
def SieveOfEratosthenes(n,primes): 
    prime = [True for i in range(n+1)] 
    p = 2
    while (p * p <= n): 
        if (prime[p] == True): 
            for i in range(p * p, n+1, p): 
                prime[i] = False
        p += 1
    for p in range(2, n): 
        if prime[p]: 
            primes.append(p)

def solve():
    p,q=MI()
    if p%q != 0:
        ans=p
    else:
        x,y=q,p
        mind=bigp
        sqrtq=int(sqrt(q))
        sp=[i for i in primes if i<=sqrtq]+[bigp]
        for i in sp:
            j=i
            if x==1:
                break
            qe=0
            while x%j==0:
                qe+=1
                x=x//j
            if i==bigp:
                qe,j=1,x
            if qe>0:
                pe=qe
                y=y//pow(j,qe)
                while y%j==0:
                    pe+=1
                    y=y//j
                mind=min(mind,pow(j,pe-qe+1))
        ans=p//mind
    stdout.write(str(ans)+"\n")

SieveOfEratosthenes(32000,primes)
t=II()
for _ in range(t):
    solve()
```