Tree Queries
Description
Since Hayate didn't get any Christmas presents from Santa, he is instead left solving a tree query problem.
Hayate has a tree with $n$ nodes.
Hayate now wants you to answer $q$ queries. Each query consists of a node $x$ and $k$ other additional nodes $a_1,a_2,\ldots,a_k$. These $k+1$ nodes are guaranteed to be all distinct.
For each query, you must find the length of the longest simple path starting at node $x^\dagger$ after removing nodes $a_1,a_2,\ldots,a_k$ along with all edges connected to at least one of nodes $a_1,a_2,\ldots,a_k$.
$^\dagger$ A simple path of length $k$ starting at node $x$ is a sequence of distinct nodes $x=u_0,u_1,\ldots,u_k$ such that there exists a edge between nodes $u_{i-1}$ and $u_i$ for all $1 \leq i \leq k$.
The first line contains two integers $n$ and $q$ ($1 \le n, q \le 2 \cdot 10^5$) — the number of nodes of the tree and the number of queries.
The following $n - 1$ lines contain two integers $u$ and $v$ ($1 \le u, v \le n$, $u \ne v$) — denoting an edge between nodes $u$ and $v$. It is guaranteed that the given edges form a tree.
The following $q$ lines describe the queries. Each line contains the integers $x$, $k$ and $a_1,a_2,\ldots,a_k$ ($1 \leq x \leq n$, $0 \leq k < n$, $1 \leq a_i \leq n$) — the starting node, the number of removed nodes and the removed nodes.
It is guaranteed that for each query, $x,a_1,a_2,\ldots,a_k$ are all distinct.
It is guaranteed that the sum of $k$ over all queries will not exceed $2 \cdot 10^5$.
For each query, output a single integer denoting the answer for that query.
Input
The first line contains two integers $n$ and $q$ ($1 \le n, q \le 2 \cdot 10^5$) — the number of nodes of the tree and the number of queries.
The following $n - 1$ lines contain two integers $u$ and $v$ ($1 \le u, v \le n$, $u \ne v$) — denoting an edge between nodes $u$ and $v$. It is guaranteed that the given edges form a tree.
The following $q$ lines describe the queries. Each line contains the integers $x$, $k$ and $a_1,a_2,\ldots,a_k$ ($1 \leq x \leq n$, $0 \leq k < n$, $1 \leq a_i \leq n$) — the starting node, the number of removed nodes and the removed nodes.
It is guaranteed that for each query, $x,a_1,a_2,\ldots,a_k$ are all distinct.
It is guaranteed that the sum of $k$ over all queries will not exceed $2 \cdot 10^5$.
Output
For each query, output a single integer denoting the answer for that query.
7 7
1 2
1 3
3 4
2 5
2 6
6 7
2 0
2 1 1
2 2 1 6
3 1 4
3 1 1
5 0
5 2 1 6
4 4
1 2
1 3
2 4
2 1 3
3 1 4
2 1 4
2 3 1 3 4
3
2
1
4
1
4
1
1
2
2
0
Note
In the first example, the tree is as follows:
In the first query, no nodes are missing. The longest simple path starting from node $2$ is $2 \to 1 \to 3 \to 4$. Thus, the answer is $3$.
In the third query, nodes $1$ and $6$ are missing and the tree is shown below. The longest simple path starting from node $2$ is $2 \to 5$. Thus, the answer is $1$.
