Communication Channel

There is a communication channel with $N+1$ stations (numbered $0$ through $N$). Station $0$ wants to send a message to station $N$. You may install memory disks at up to $K$ of the stations $1, 2, \ldots, N-1$. Let's denote the increasing sequence of stations at which memory disks are installed by $(v_1, v_2, \ldots, v_k)$, where $k \le K$ is the number of such stations, and let $v_0 = 0$ and $v_