Eat Rock!

Rockeater Rocky is on a mission to eat rocks! There are $N$ rocks on the $X$-axis. The $i^{th}$ of these rocks is at position $X_i$ and has weight $W_i$. All the $W_i$ are **distinct**. Consider a subset $S$ consisting of $k$ rocks. Rocky will eat the rocks in $S$ as follows: - Let $i_1, i_2, \ldots, i_k$ be the list of indices of rocks in $S$, sorted in **ascending** order of weight. - Th