Leetcode 858. Mirror Reflection

Given a square room of side p and a laser from the southwest corner that first hits the east wall q units up, determine which corner receptor (0, 1, or 2) the ray will hit first after reflections. Algorithmically, this reduces to finding the smallest k with k*q divisible by p (via gcd/lcm) and using the parity of the resulting vertical/horizontal multiples to identify the receptor.