Gravity Golf

Let $B$ be a **binary** grid with $K$ rows and $N$ columns. The cell at the intersection of the $i$-th row and $j$-th column is denoted $(i, j)$. $B$ represents a golf course, where each cell is empty (if it contains a $0$) or blocked (if it contains a $1$). The cells $(1, 1)$ and $(K, N)$ are both empty. Suppose your *stroke power* is $P$. You will then play a game of golf on this course as