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 collections import Counter

nn = int(input())

def get_primes(up_to):
    res = []
    for p in range(2, up_to+1):
        flag = False
        for q in res:
            if q*q > p: 
                break
            if p%q == 0:
                flag = True
                break
        if not flag:
            res.append(p)
    return res
 
primes = get_primes(int(1000000000**0.5))
primes_set = set(primes)

def get_prime_divisors(x):
    res = Counter()
    if x in primes_set:
        res[x] += 1
        return res
    for prime in primes:
        while x%prime == 0:
            x = x//prime
            res[prime] += 1
        if x in primes_set:
            res[x] += 1
            return res
    if x > 1:
        res[x] += 1
    return res

def get_fix_prime_divisors(x, fix_primes):
    res = Counter()
    for prime in fix_primes:
        while x%prime == 0:
            x = x//prime
            res[prime] += 1
    return res

def main(p, q):
    q_primes = get_prime_divisors(q)
    p_primes = get_fix_prime_divisors(p, q_primes)
    minim = 10E18
    for prime in q_primes:
        diff = p_primes[prime] - q_primes[prime]
        if diff < 0:
            return(p)
        minim = min(minim, prime**(diff+1))
    return p//minim
   
for _ in range(nn):
    p, q = [int(s) for s in input().split()]
    print(main(p, q))