Number Walks

You are given an array $A$ of $N$ integers, and an integer $K$ such that $1 \le A_i \le K$, and each integer $1, 2 \ldots, K$ appears at least once in the array $A$. Suppose you start at some position $S$ ($1 \le S \le N$), solve the following problem: - A sequence of $(K + 1)$ integers, $B_0, B_1, B_2, \ldots, B_{K}$ is called *good* if it satisfies the following conditions: - $B_0 = S$