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 $$$1 \leq i \leq k$$$.
Input Format:
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 Format:
For each query, output a single integer denoting the answer for that query.
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 $$$1$$$.