1444A · Division

Problem: 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 $q_i$.

Input Format: 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.

Output Format: 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.

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 $q_2 = 6$.