Rigged Game

In a video game country, there are $N$ cities connected by $N-1$ bi-directional roads, forming a tree network. The $i_{th}$ city has an integer associated with it, called difficulty $D_i$. A game map is represented by a pair of integers $(X,Y)$, such that $(1\leq X\leq N)$ and $(0 \leq Y \leq {N-1})$. All nodes within a distance $Y$ from the node $X$ are included in this game map. (Note that the