P9864 [POI 2021/2022 R2] age

Translated from [POI2021~2022R2 Day1T1](https://szkopul.edu.pl/problemset/problem/weKRWGa1NgLNHT1WLDo5ohuH/statement/)。

There is a country with $n$ cities. We can view it as a tree with $n-1$ roads. One day, you suddenly decide to place $k$ people in different cities. The people and their movement must satisfy the following rules: - Each day, only one person may move, and they can move to a neighboring city connected by a road. - Suppose there are two people $a,b$. If city $i$ has been visited by $a$, then $b$ is not allowed to visit city $i$. Initially, you know the positions of the people. Each person starts in a different city, and that city is considered “already visited”. You need to plan a valid visiting scheme. Find the minimum number of days needed so that all cities are visited by someone.

The first line contains two integers $n,k\ (1 \leq n \leq 5 \times 10^5, 1 \leq k \leq n)$。 The second line contains $k$ integers, representing the initial positions of the people. Then follow $n-1$ lines, each describing a road $(a_i,b_i)\ (1 \leq a_i,b_i \leq n)$。

Output the minimum number of days。

Explanation of the sample:  The subtasks are as follows: | Subtask ID | Special property | Score | | :----------: | :----------: | :----------: | | $1$ | $n \leq 10$ | $6$ | | $2$ | $n \leq 20$ | $13$ | | $3$ | $n \leq 2000$ | $27$ | | $4$ | $k=1$ | $10$ | | $5$ | $k=2$ | $7$ | | $6$ | The input is a chain | $7$ | | $7$ | No special property | $30$ | Subtask $0$ is the sample。 Translated by ChatGPT 5