Travelling Caterpillar

Lilith is a hungry caterpillar! From her vantage point at the root of a tree, she has identified some leaves she wishes to munch before returning to the root. She wants to finish munching all of them as quickly as possible so that she will grow into a plump, buttery butterfly.

The tree Lilith occupies is a bit unusual. We can view it as a collection of nodes, where some of the nodes contain leaves that Lilith wishes to munch. Each branch connects exactly two nodes together. Between every pair of nodes, there is exactly one way to travel from one to the other.

Figure 1: Lilith's route through the tree.

The first line contains two integers $N$ ($1 \le N \le 1000$), the number of nodes in the tree, and $K$ ($1 \le K \le N$), the number of leaves Lilith wants to munch.

The next $N-1$ lines describe the branches. The $i$th line contains three integers $s_i$, $t_i$ ($0 \le s_i, t_i < N$, $s_i \ne t_i$), and $d_i$ ($0 \le d_i \le 10^6$). This means there is a branch between nodes $s_i$ and $t_i$ that takes $d_i$ time to cross. If the tree is rooted at node $0$, then $s_i$ is the parent of $t_i$, so $s_i$ lies on the unique path from $0$ to $t_i$. Lilith always starts at the root node $0$.

The last line contains $K$ distinct integers $a_1, \dots, a_K$ ($0 \le a_i < N$), the nodes that contain leaves Lilith wants to munch.

Print the length of the shortest path that starts and ends at the root along the branches and lets Lilith munch all the leaves.