Carry Bed

Chef has a sequence $A_1, A_2, \ldots, A_N$. Let's define a function $f(l, r)$ in the following way: - If $1 \le l \le r \le N$, then $f(l, r)$ is the maximum of $A_l, A_{l+1}, \ldots, A_r$. - Otherwise, $f(l, r)$ is $0$. Chef wants to choose a subset $S$ of the set of indices $\{1, 2, \ldots, N\}$ such that $|S| \ge K$. Let's define $C = \sum_{i \in S}\sum_{j \in S} f(i, j)$. Can you help