National Junior Problem 9

[Kazi Nadid Hossain]

In the cartesian coordinate system, four points (0; 0); (20; 0); (20; 19) and (0; 19) are used
as vertices to draw a rectangle. At first, a ball with negligible size is at the (0; 0) point. It then started
to move towards the point (2; 1). Every second, the ball passes the amount of distance between (0; 0)
to (2; 1). If it collides with one side of the rectangle, it follows the law of reflection and comes back
to the rectangle. If it collides with a corner, it again follows the law of reflection and comes back in
the direction it went in. Until the 2019th second, how many times will the ball collide with a corner
point?