Two Chess Pieces

# Two Chess Pieces ## 题目描述 Cirno\_9baka 有一棵包含 $n$ 个节点的树。他愿意把它与你分享，这意味着你可以对它进行一些操作。 最初，树的 $1$ 号节点上有两个棋子。对每个操作，您可以选择任意一个棋子，并将其移动到相邻节点。你需要确保两个棋子之间的距离不会超过 $d$。 给你两个序列，分别表示两个棋子需要经过的节点（可以以**任何顺序**经过）。最终，它们必须回到根节点。作为一个好奇的男孩，Cirno\_9baka 想知道最少操作次数。 ## 输入格式 第一行包含两个整数 $n$ 和 $d$（$2\le d\le n\le 2\cdot 10^5$）。 以下 $n-1$ 行的第 $i$ 行包含两个整数 $ u_i, v_i $ $ (1 \le u_i, v_i \le n) $，表示节点 $ u_i, v_i $ 之间的边。 保证这些边形成一棵树。 下一行包含一个整数 $m_1$（$1\le m_1\le n$）和 $m_1$ 个整数 $a_1，a_2，\ldots，a_{m_1}$（$1\le a_i\le n$，所有$a_i$都是不同的）- 第一个棋子需要经过的节点序列。 第二行包含一个整数$m_2$（$1\le m_2\le n$）和 $m_2$ 个整数 $b_1，b_2，\ldots，b_{m_2}$（$1\le b_i\le n$，所有$b_i$都是不同的）-第二棋子需要经过的节点序列。 ## 输出格式 输出一个整数 - 最小操作次数。

Cirno\_9baka has a tree with $ n $ nodes. He is willing to share it with you, which means you can operate on it. Initially, there are two chess pieces on the node $ 1 $ of the tree. In one step, you can choose any piece, and move it to the neighboring node. You are also given an integer $ d $ . You need to ensure that the distance between the two pieces doesn't ever exceed $ d $ . Each of these two pieces has a sequence of nodes which they need to pass in any order, and eventually, they have to return to the root. As a curious boy, he wants to know the minimum steps you need to take.

The first line contains two integers $ n $ and $ d $ ( $ 2 \le d \le n \le 2\cdot 10^5 $ ). The $ i $ -th of the following $ n - 1 $ lines contains two integers $ u_i, v_i $ $ (1 \le u_i, v_i \le n) $ , denoting the edge between the nodes $ u_i, v_i $ of the tree. It's guaranteed that these edges form a tree. The next line contains an integer $ m_1 $ ( $ 1 \le m_1 \le n $ ) and $ m_1 $ integers $ a_1, a_2, \ldots, a_{m_1} $ ( $ 1 \le a_i \le n $ , all $ a_i $ are distinct) — the sequence of nodes that the first piece needs to pass. The second line contains an integer $ m_2 $ ( $ 1 \le m_2 \le n $ ) and $ m_2 $ integers $ b_1, b_2, \ldots, b_{m_2} $ ( $ 1 \le b_i \le n $ , all $ b_i $ are distinct) — the sequence of nodes that the second piece needs to pass.

Output a single integer — the minimum steps you need to take.

4 2
1 2
1 3
2 4
1 3
1 4

6

4 2
1 2
2 3
3 4
4 1 2 3 4
1 1

8

In the first sample, here is one possible sequence of steps of length $ 6 $ . - The second piece moves by the route $ 1 \to 2 \to 4 \to 2 \to 1 $ . - Then, the first piece moves by the route $ 1 \to 3 \to 1 $ . In the second sample, here is one possible sequence of steps of length $ 8 $ : - The first piece moves by the route $ 1 \to 2 \to 3 $ . - Then, the second piece moves by the route $ 1 \to 2 $ . - Then, the first piece moves by the route $ 3 \to 4 \to 3 \to 2 \to 1 $ . - Then, the second piece moves by the route $ 2 \to 1 $ .