# Auxiliary Set

Time Limit: 9000/4500 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

## Description

Given a rooted tree with n vertices, some of the vertices are important.

An auxiliary set is a set containing vertices satisfying at least one of the two conditions：

$\bullet$It is an important vertex
$\bullet$It is the least common ancestor of two different important vertices.

You are given a tree with n vertices (1 is the root) and q queries.

Each query is a set of nodes which indicates the unimportant vertices in the tree. Answer the size (i.e. number of vertices) of the auxiliary set for each query.

## Input

The first line contains only one integer T ($T \leq 1000$), which indicates the number of test cases.

For each test case, the first line contains two integers n ($1 \leq n \leq 100000$), q ($0 \leq q \leq 100000$).

In the following n -1 lines, the i-th line contains two integers $u_i,v_i (1\leq u_i,v_i \leq n)$ indicating there is an edge between $u_i$i and $v_i$ in the tree.

In the next q lines, the i-th line first comes with an integer $m_i (1 \leq m_i \leq 100000)$ indicating the number of vertices in the query set.Then comes with mi different integers, indicating the nodes in the query set.

It is guaranteed that $\sum^q_{i=1} m_i \leq 100000$.

It is also guaranteed that the number of test cases in which $n \geq 1000$  or $\sum_{i=1}^{q} m_i \geq 1000$ is no more than 10.

## Output

For each test case, first output one line "Case #x:", where x is the case number (starting from 1).

Then q lines follow, i-th line contains an integer indicating the size of the auxiliary set for each query.

## Sample Input

1
6 3
6 4
2 5
5 4
1 5
5 3
3 1 2 3
1 5
3 3 1 4

## Sample Output

Case #1:
3
6
3
Hint

For the query {1，2, 3}:
•node 4, 5, 6 are important nodes For the query {5}：
•node 1，2, 3, 4, 6 are important nodes
•node 5 is the lea of node 4 and node 3 For the query {3, 1，4}:
• node 2, 5, 6 are important nodes


wange2014

## Source

2016CCPC东北地区大学生程序设计竞赛 - 重现赛