Colosseum

For a permutation$^\dagger$ $P$ of the integers $1$ to $N$, and a parameter $K$, we define its *winner*, denoted $\text{win}(P, K)$, as the result of the following process: - Let $x = 1$ initially. - For each index $i$ from $2$ to $N$, in order: - If $P_i + K \geq P_x$, set $x$ equal to $i$. $\text{win}(P, K)$ is then defined to be the final value of $x$, after the process ends. --- You're