Phonomenal Reviews

Jo is a blogger who reviews restaurants. Today she wants to visit every Vietnamese pho restaurant in the Waterloo area and decide which one is best.

Waterloo has $N$ restaurants, numbered $0$ to $N-1$. Only $M$ of them are pho restaurants. Jo may start at any restaurant. Waterloo has $N-1$ roads, and each road connects exactly two restaurants. Using only these roads, Jo can travel from any restaurant to any other restaurant. Travelling along one road takes exactly 1 minute.

In computer science a road network with this structure is called a tree. Here are three examples of trees.

Every tree has this property. Between any two points there is exactly one path that repeats no road.

What is the least amount of time Jo has to spend travelling on roads to visit all of the pho restaurants?

The first line contains two integers $N$ and $M$ ($2 \le M \le N \le 100000$).

The second line contains $M$ distinct integers, the numbers of the pho restaurants.

Each of the next $N-1$ lines contains two integers. The $a_i$ and $b_i$ on line $i$ ($0 \le a_i, b_i \le N-1$) describe a road between restaurant $a_i$ and restaurant $b_i$.

Print one line with one integer, the minimum number of minutes Jo has to spend travelling on roads in order to visit every pho restaurant.