Point Of Impact

You are playing a Billiards-like game on an $N \times N$ table, which has its four corners at the points $\{(0, 0), (0, N), (N, 0),$ and $(N, N)\}$. You start from a coordinate $(x,y)$, $(0 < x < N, 0 < y < N)$ and shoot the ball at an angle $45^{\circ}$ with the horizontal. On hitting the sides, the ball continues to move with the same velocity and ensuring that the angle of incidence is equal