Amphibian Escape

Chef is building a robot frog, which he would like to be able to climb out of a well quickly. The well has a height of $H$ units. Initially, the frog is placed at the bottom of the well. Let $A$ denote the *jumping power* of the frog, and $B$ denote the *slipperiness* of the well's wall. The frog is initially at position $X = 0$. Every second, the following two steps happen in order: - First