CF1774E Two Chess Pieces

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.

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 $ .