Draft Picks

$N$ people are preparing to play a card game. The people are numbered $1$ to $N$. There are $K$ cards, with exactly one card having strength $x$ for each $1 \le x \le K$. In an attempt to keep things fair, the players decide to pick cards in a *snake draft*. This means the process is as follows: - First, player $1$ will pick one card, then player $2$ will pick one card, then player $3$, and s