Exclusion-Inclusion

You are given an array $A = [A_1, A_2, \ldots, A_N]$ containing $N$ integers. For a fixed parameter $K$ ($1 \leq K \leq N$), consider the following process: - You have a score, initially equal to $0$. - There is a bucket, initially containing the elements $A_1, A_2, \ldots, A_{K-1}$. - For each $i$ from $K$ to $N$: - Insert $A_i$ into the bucket. - Then, choose one element from the bucket