Spring cleaning

This tree has $N$ nodes numbered from 1 to $N$, connected by $N-1$ edges. The edges have gathered too much dust, so Flóra's mother decided to clean them.

Cleaning the edges of an arbitrary tree is done by repeating the following process. Choose two different leaves (a node is a leaf if it is connected to exactly one other node by an edge), and clean every edge on the shortest path between them. If this path has $d$ edges, the cost of cleaning it is $d$.

To avoid harming the leaves, each leaf may be chosen at most once. A tree is clean when all of its edges are cleaned. The cost is the sum of the costs of all cleaned paths.

Flóra thinks the tree is too small and simple, so she imagines $Q$ variations of it. In the $i$-th variation, she adds a total of $D_i$ extra leaves to the original tree. For each new leaf, she picks a node of the original tree and connects that node to the new leaf with an edge. Some nodes may stop being leaves after this step.

For each of the $Q$ variations, find the minimum cost required to clean the tree. Each variation starts from the original tree.

The first line contains two integers $N$ and $Q$.

Each of the next $N-1$ lines contains two integers $u$ and $v$, meaning that nodes $u$ and $v$ are connected by an edge.

Each of the next $Q$ lines describes one variation. The first integer on the $i$-th line is $D_i$, followed by $D_i$ integers $a_j$. Each $a_j$ is the node to which a new leaf is attached. Several new leaves may be attached to the same node.

Print $Q$ lines. On the $i$-th line, print the minimum cost to clean the tree in the $i$-th variation. If the tree cannot be cleaned, print $-1$.

$3 \le N \le 10^5$

$1 \le Q \le 10^5$

$1 \le u, v \le N$

$1 \le D_i \le 10^5$ for all $i$

$\sum D_i \le 10^5$ for $1 \le i \le Q$

$1 \le a_j \le N$ for all $j$ in every variation

The picture shows the second variation.

One possible solution is to clean the paths between leaves 1 and 6, A and 7, and B and 3.