The Coordinate Plane · Superchallenge problem

A ball rolls inside a rectangular box whose corners are $(0, 0)$, $(6, 0)$, $(6, 4)$ and $(0, 4)$. It starts at the corner $(0, 0)$ and each second it moves $1$ unit right and $1$ unit up. When it hits a side of the box it bounces: hitting a left or right side switches it between moving right and moving left, and hitting the top or bottom switches it between moving up and moving down. At which corner does the ball first arrive at a corner again? Write the corner as (x, y).