A13936. 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?

The first line contains an integer $t$ ( $1 \le t \le 50$ ) — the number of pairs.

Each of the following $t$ lines contains two integers $p_i$ and $q_i$ ( $1 \le p_i \le 10^{18}$ ; $2 \le q_i \le 10^{9}$ ) — the $i$ -th pair of integers.

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.

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 $6$ .