Vlad and Unfinished Business
Contest: Codeforces Round 787 (Div. 3)
Difficulty rating: 1800
Tags: dfs and similar, dp, greedy, trees

Vlad and Nastya live in a city consisting of $$$n$$$ houses and $$$n-1$$$ road. From each house, you can get to the other by moving only along the roads. That is, the city is a tree.

Vlad lives in a house with index $$$x$$$, and Nastya lives in a house with index $$$y$$$. Vlad decided to visit Nastya. However, he remembered that he had postponed for later $$$k$$$ things that he has to do before coming to Nastya. To do the $$$i$$$-th thing, he needs to come to the $$$a_i$$$-th house, things can be done in any order. In $$$1$$$ minute, he can walk from one house to another if they are connected by a road.

Vlad does not really like walking, so he is interested what is the minimum number of minutes he has to spend on the road to do all things and then come to Nastya. Houses $$$a_1, a_2, \dots, a_k$$$ he can visit in any order. He can visit any house multiple times (if he wants).

Input format:
The first line of input contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of input test cases. There is an empty line before each test case.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 2\cdot 10^5$$$) — the number of houses and things, respectively.

The second line of each test case contains two integers $$$x$$$ and $$$y$$$ ($$$1 \le x, y \le n$$$) — indices of the houses where Vlad and Nastya live, respectively.

The third line of each test case contains $$$k$$$ integers $$$a_1, a_2, \dots, a_k$$$ ($$$1 \le a_i \le n$$$) — indices of houses Vlad need to come to do things.

The following $$$n-1$$$ lines contain description of city, each line contains two integers $$$v_j$$$ and $$$u_j$$$ ($$$1 \le u_j, v_j \le n$$$) — indices of houses connected by road $$$j$$$.

It is guaranteed that the sum of $$$n$$$ for all cases does not exceed $$$2\cdot10^5$$$.

Output format:
Output $$$t$$$ lines, each of which contains the answer to the corresponding test case of input. As an answer output single integer — the minimum number of minutes Vlad needs on the road to do all the things and come to Nastya.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Note:
Tree and best path for the first test case:

$$$1 \rightarrow 2 \rightarrow 1 \rightarrow 3$$$

Tree and best path for the second test case:

$$$3 \rightarrow 1 \rightarrow 3 \rightarrow 5 \rightarrow 2 \rightarrow 5 \rightarrow 6 \rightarrow 5$$$

Tree and best path for the third test case:

$$$3 \rightarrow 5 \rightarrow 2$$$

Example input:
3
3 1
1 3
2
1 3
1 2
6 4
3 5
1 6 2 1
1 3
3 4
3 5
5 6
5 2
6 2
3 2
5 3
1 3
3 4
3 5
5 6
5 2

Example output:
3
7
2

Editorial:
To begin with, we will hang the tree by the vertex $$$x$$$. In fact, we want to go from the root to the top of $$$y$$$, going off this path to do things and coming back. At one vertex of the path, it is advantageous to get off it in all the necessary directions and follow it further. So we will go $$$1$$$ once for each edge leading to $$$y$$$ and $$$2$$$ times for each edge leading to some of the cases, but not leading to $$$y$$$.
Let's match each vertex with an edge to its ancestor. If the edge of a vertex leads to $$$y$$$, then $$$y$$$ is in the subtree of this vertex, similarly with vertices with cases. It is necessary for each vertex to determine whether there is a vertex $$$y$$$ in its subtree and whether there is a vertex from the array $$$a$$$, this can be done using a depth-first search, then we will calculate the answer according to the rules described above.