Stick Break

Chef has a stick of length $L$. Chef wants to break the stick into $K$ parts such that each part has a non-zero length. Let the lengths of the $K$ parts be $A_1, A_2, \ldots, A_K$ (Note that $A_1 + A_2 + \ldots + A_K = L$ and $A_i$ is a **positive integer** for all $i$). Chef wants to minimize the value of $\displaystyle \sum_{i = 1}^{K - 1}|A_{i + 1} - A_i|$. Can you help Chef? (Here $|x|$ deno