Dual Distance Disparity

You are given a tree (a simple connected acyclic graph) with $N$ vertices, as well as two integers $K$ and $D$. The *distance* between two vertices $u$ and $v$ in the tree, denoted $\text{dist}(u, v)$, is defined to be the number of edges on the (unique) path between $u$ and $v$ in the tree. You would like to color each vertex of the tree either red or blue. Exactly $K$ vertices must be colore