Tree Tripping

A tree with $N$ nodes is given. Process $Q$ queries of the following form.

• k u_1 u_2 ... u_k: Choose any node in the tree. Print the minimum possible sum of distances from the chosen node to nodes $u_1, u_2, \dots, u_k$.

The first line contains the number of nodes $N$ and the number of queries $Q$, separated by a space. ($1 \le N \le 300000$; $1 \le Q \le 500000$)

The next $N-1$ lines each contain two distinct node numbers $a$ and $b$, separated by a space, which form an edge of the tree. ($1 \le a, b \le N$)

The next $Q$ lines each contain a query k u_1 u_2 ... u_k. ($1 \le k \le N$; $1 \le u_i \le N$; $i \ne j$ implies $u_i \ne u_j$)

The sum of $k$ over all queries is at most $500000$.

For each query, print the minimum sum of distances between the chosen node and the given nodes, one per line.