Breaking Bricks

For her next karate demonstration, Ada will break some bricks. Ada stacked three bricks on top of each other. Initially, their widths (from top to bottom) are $W_1, W_2, W_3$. Ada's strength is $S$. Whenever she hits a stack of bricks, consider the largest $k \ge 0$ such that the sum of widths of the topmost $k$ bricks does not exceed $S$; the topmost $k$ bricks break and are removed from th