Bouncing Ball Steps

There is a ball at the top-left corner of an n \times m grid. The rows of the grid are numbered 1,2,\dots,n, and the columns are numbered 1,2,\dots,m. The ball is initially moving diagonally away from the top-left corner. At every step, it moves one cell. Whenever the ball hits the border of the grid, it changes its direction. What is the location of the ball after k steps and how many times has