Story

"May the world... please forget me..."

Problem Statement

There is a tree with $N$ vertices, numbered $1, 2, \cdots, N$. The $i$-th edge connects vertex $A_i$ and vertex $B_i$.

Each vertex has a value called its purity; the purity of vertex $i$ is $P_i$.

Currently, some vertices of this tree are contaminated. At time $0$, the contaminated vertices are the $M$ vertices $C_1, C_2, \cdots, C_M$.

From now on, at each time represented as time $t$ for a positive integer $t$, the following event occurs.

• Let $S$ be the set of vertices that are contaminated at that moment. For every $x\in S$, all vertices adjacent to vertex $x$ that are not yet contaminated become contaminated.

In addition, at each time represented as time $t-0.5$ for a positive integer $t$, you perform the following action.

• If there exist vertices that are leaves and are not contaminated at that moment, choose the one with the maximum purity among them, and remove the chosen vertex and the $1$ edge coming out of it. If no such leaf exists, do nothing.

Find the sum of the purity over all vertices you remove at or before time $10^{100}$.

Input

$N\ M$
$P_1\ P_2\cdots\ P_N$
$A_1\ B_1$
$A_2\ B_2$
$\vdots$
$A_{N-1}\ B_{N-1}$
$C_1\ C_2\ \cdots\ C_M$

• $2\leq N\leq 10^5$
• $1\leq M\leq N$
• $1\leq P_i\leq 10^9$
• $P_1, P_2, \cdots, P_N$ are pairwise distinct.
• $1\leq A_i, B_i\leq N$
• $1\leq C_i\leq N$
• The values in $C$ are pairwise distinct.
• All input values are integers.

Output

Let $S$ be the sum of the purity over all vertices you remove at or before time $10^{100}$. Output it on one line in the following format.

$S$

Print a newline at the end.

Sample

5 1
3 2 4 1 5
1 2
1 3
3 4
3 5
1

6