A16186. Minimum Maximum Distance

You have a tree with $n$ vertices, some of which are marked. A tree is a connected undirected graph without cycles.

Let $f_i$ denote the maximum distance from vertex $i$ to any of the marked vertices.

Your task is to find the minimum value of $f_i$ among all vertices.

For example, in the tree shown in the example, vertices $2$ , $6$ , and $7$ are marked. Then the array $f(i) = [2, 3, 2, 4, 4, 3, 3]$ . The minimum $f_i$ is for vertices $1$ and $3$ .

The first line contains an integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.

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 vertices in the tree and the number of marked vertices, respectively.

The second line of each test case contains $k$ integers $a_i$ ( $1 \le a_i \le n, a_{i-1} < a_i$ ) — the indices of the marked vertices.

The next $n - 1$ lines contain two integers $u_i$ and $v_i$ — the indices of vertices connected by the $i$ -th edge.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, output a single integer — the minimum value of $f_i$ among all vertices.