Apples and Snakes

Input

The first line contains two integers $n$ and $m$ $(1 \leq m \leq n \leq 2 \cdot 1 0^{5})$ (1 \le m \le n \le 2 \cdot 10^5) — the number of vertices and snakes in the tree, respectively.

The second line contains an array $a$ of length $n$ $(0 \leq a_{i} \leq 1 0^{6})$ (0 \le a_i \le 10^6) — the number of apples in each vertex.

The third line contains an array $b$ of length $m$ $(1 \leq b_{i} \leq n)$ (1 \le b_i \le n) — the indices of the vertices that have snakes.

Next, there are $n - 1$ n - 1 lines where each line contains two integers $u$ and $v$ $(1 \leq u, v \leq n, u \neq = v)$ (1 \le u, v \le n, u \neq v) — the edges between vertices $u$ and $v$ .

Output

You need to output a single integer — the maximum number of apples that can be eaten.

Examples

Example 1

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Example 2

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Note

In the first example, we will have the following tree, where the red vertices are the vertices with snakes

Then we can draw an edge between vertex $1$ and $3$ . And we will follow the next path:

$6$ $- >$ $7$ $- >$ $1$ $- >$ $3$ . Then the total number of apples will be $38$ .

In the second example, we will have the following tree, where the red vertices are the vertices with snakes

Then we can draw an edge between vertex $1$ and $3$ . And we will follow the next path:

$1$ $- >$ $3$ $- >$ $4$ . Then the total number of apples will be $19$ .

Scoring

Subtask $1$ ( $10$ points): $(n \leq 10)$ (n \le 10)
Subtask $2$ ( $20$ points): $(n \leq 100)$ (n \le 100)
Subtask $3$ ( $20$ points): (All $u$ $=$ $1$ )
Subtask $4$ ( $50$ points): $(n \leq 5000)$ (n \le 5000)
Subtask $5$ ( $60$ points): $(m = 0)$ (m = 0)
Subtask $6$ ( $70$ points): $(m \leq 10)$ (m \le 10)
Subtask $7$ ( $40$ points): (All $a_{v}$ a_v $=$ $1$ )
Subtask $8$ ( $50$ points): (All $a_{v}$ a_v $\leq$ $1$ )
Subtask $9$ ( $10$ points): (All $u$ $=$ $v$ $-$ $1$ )
Subtask $10$ ( $170$ points): Without additional constraints