Jo is a blogger, specializing in the critique of restaurants. Today,
she wants to visit all the Vietnamese Pho restaurants in the Waterloo
area, in order to determine which one is the best.

There are \(N\) restaurants in the
city of Waterloo, numbered \(0\) to
\(N-1\). However, only \(M\) of them are Pho restaurants. Jo can
choose to start at any restaurant. There are \(N-1\) roads in Waterloo, each road
connecting exactly two restaurants. It is possible to reach every
restaurant from any restaurant using these roads. It takes Jo exactly 1
minute to travel along any road.

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

One property that is true for all trees is that
there is exactly one path that does not repeat any roads between any two
points in the tree.

What is the minimal length of time that Jo needs to spend on
travelling on roads to visit all of the Pho restaurants?

\((2 \leq M \leq N \leq 100\ 000)\)
\((0 \leq a_i , b_i \leq N-1)\)
\(N \leq 100\)
\(M \leq 3\)
\(M \leq 8\)
\(M \leq N \leq 1000\)

The first line of input contains 2 integers, \(N\) and \(M\) \((2 \leq M \leq N \leq 100\ 000)\).

The second line of input contains \(M\) distinct integers indicating the
restaurants which are Pho restaurants.

The next \(N\)-1 lines contain 2
integers each. The \(i\)-th line
contains \(a_i\) and \(b_i\), \((0 \leq a_i , b_i \leq N-1)\), representing a path between the two
restaurants numbered \(a_i\) and \(b_i\).

For 3 of the 15 available marks, \(M = 2\) and \(N \leq 100\).

For an additional 3 of the 15 available marks, \(M \leq 3\) and \(N \leq 100\).

For an additional 3 of the 15 available marks, \(M \leq 8\) and \(N \leq 100\).

For an additional 4 of the 15 available marks, \(M \leq N \leq 1000\).

Your program should output one line, containing one integer - the
minimum amount of time Jo needs to spend travelling on roads in order to
visit all Pho restaurants, in minutes.

생성자가 기록되지 않았습니다.

출처 CCC 2016 Senior