Minimum Ugliness

You are given a tree with $N$ nodes where the nodes are numbered from $1$ to $N$. The tree is rooted at node $1$. The shortest distance between two nodes $u$ and $v$ is the number of edges in the unique shortest path between $u$ and $v$ in the tree. Let it be denoted by $\text{dist}(u, v)$. You have $Q$ queries of the following type: For the $i$-th query, let $A_i$ be a set of $K_i$ nodes in th