Median

You are given an integer sequence $A_1, A_2, \dots, A_N$ and integers $K$ and $M$. For $1 \le i \le j \le N$, let's define $S(i, j)$ as the number of ways to choose exactly $K$ elements of the contiguous subsequence $A_i, A_{i+1}, \dots, A_j$ in such a way that the median of these $K$ elements is $\ge M$. Find the sum of $S(i, j)$ over all $i, j$ such that $1 \le i \le j \le N$. Since this sum ma