Background

Translated from POI2021~2022R2 Day1T1。

Problem Description

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.

Input Format

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 Format

Output the minimum number of days。

6 2
2 6
1 2
2 3
2 4
5 4
5 6

5

Hint

Explanation of the sample:

The subtasks are as follows:

Subtask $0$ is the sample。

Translated by ChatGPT 5