There is a square room with walls of length p. Each of the corners, except for the starting corner, contains a receptor:

• Receptor $0$ is located at $(`p`, 0)$

• Receptor $1$ is located at $(`p`, `p`)$

• Receptor $2$ is located at $(0, `p`)$

A laser ray originates from the southwest corner $(0, 0)$ and travels in a straight line until it first hits the opposite wall at coordinates $(`p`, `q`)$. The ray continues to bounce off the walls according to the law of reflection until it strikes one of the receptors.

Return the identifier of the receptor ($0$, $1$, or $2$) that the ray encounters first.

Note: It is guaranteed that the ray will eventually strike a receptor.

Constraints:

• $1 \leq$ q $\leq$ p $\leq 1000$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.