Delete The Array

Given an integer $K$, consider an array $A$ of size $N$. You can perform the following operation on the array: - Select an integer $X$; - Remove all elements from $A$ satisfying $X \le A_i \lt X + K$. Let $f(A)$ denote the **minimum** number of such operations needed to make the array $A$ empty, i.e. delete all of its elements. Given integers $N$ and $M$, find the sum of $f(A)$ over all **stric