Delete For Fun

You are given a circular binary string $S$ of length $N$. That is, position $1$ is adjacent to positions $2$ and $N$, and in general position $i$ is adjacent to $(i-1)$ and $(i+1)$ (with indices taken modulo $N$). You are also given a starting index $K$. You must delete all $N$ characters from the string, one at a time, following these rules: - Your score starts at $0$. - The first deletion