Bouncing Inside a Box

A square box is fixed in place in the $x y$ plane, with its corners at $(x,y)$ values of $(0,0)$ , $(1,0)$ , $(0,1)$ , and $(1,1)$ . A ball is initially at $(0.3,0.8)$ , with a velocity vector $(v_x,v_y)$ of $(13,7)$ . The ball bounces off of the sides of the box.

What is the sum of the $x$ and $y$ coordinates of the ball on its 1000th bounce?

Details and Assumptions:
- When the ball bounces off of a horizontal surface, its $y$ velocity is negated and its $x$ velocity is preserved.
- When the ball bounces off of a vertical surface, its $x$ velocity is negated and its $y$ velocity is preserved.
- There are no forces at play when the ball is traversing the interior of the box