Safety in Treeland

The kingdom of Treeland consists of $N$ cities (numbered $1$ through $N$) connected by $N-1$ bidirectional roads in such a way that there is a path between each pair of cities. In order to increase security in Treeland, the government decided to set up police offices in $K$ of its cities. For each valid $i$, the $i$-th office is in city $V_i$ and it has a *radius of efficiency* $R_i$. Let's