Another Game

Alice and Bob have decided to play yet another game. Alice will give Bob a **non-negative** integer $K$ and a permutation$^\dagger$ $P$ of length $N$. Bob's goal is to sort the permutation $P$ in ascending order. To achieve this, Bob can perform the following operations however many times he likes: - Choose two indices $i$ and $j$ such that $P_i + P_j \leq K$, and swap $P_i$ and $P_j$. Alice