Distance Sum

For a given array $A$ of length $N$, we define $f(A)$ in the following way: - Consider a directed graph on $N$ vertices labelled $1$, $2$, $\ldots$, $N$. - There exist a directed edge $i \rightarrow j$ if and only if $i < j \le i + A_i$. - $f(A)$ is defined as the smallest number of edges on a directed path from vertex $1$ to vertex $N$. You are given integers $N$ and $P$, and your task is