Subtree Center

You are given a tree with $N$ nodes (numbered $1$ through $N$) and $Q$ queries (numbered $1$ through $Q$). For each valid $i$, in the $i$-th query, you are given $K_i$ nodes $x_1, x_2, \ldots, x_{K_i}$. Consider the smallest subtree which contains all of these nodes; you should find all centers of this subtree. A node is called a *center* of a tree if it lies in the middle of at least one longest