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.
t = int(input())
for _ in range(t):
    p, q = map(int, input().split())
    if p % q:
        print(p)
    else:
        d = 2
        while d * d <= q and q % d:
            d += 1
        if d * d > q:
            d = q
        primes = [d]
        deg_q = [1]
        r = q // d
        while r % d == 0:
            r //= d
            deg_q[0] += 1
        if d == 2:
            d = 3
        else:
            d += 2
        while r > 1:
            while d * d <= r and r % d:
                d += 2
            if d * d > r:
                d = r
            primes.append(d)
            deg_q.append(0)
            while r % d == 0:
                r //= d
                deg_q[-1] += 1
            d += 2
        deg_p = []
        r = p
        for pr in primes:
            deg_p.append(0)
            while r % pr == 0:
                r //= pr
                deg_p[-1] += 1
        rec = p
        for i in range(len(primes)):
            n = int(primes[i] ** (deg_p[i] - deg_q[i] + 1))
            if n < rec:
                rec = n
        print(p // rec)

