Problem Description

Neko has a tree with $n$ nodes.
There are $m$ key nodes on tree. Neko want to you to selecte some key nodes satisfying the distance between any two selected nodes less than or equal to $k$.
Neko thinks this work is too easy,so Neko want to know how many different way for selecting nodes.
Calculate the answer after mod $10^9+7$.
Note that you have to select at least one key node.

Input

The first line contains three integers $n, m, k(1 \leq n,m,k \leq 5000)$.
The next $n-1$ line, each line contains two integers $u, v$,indicating there is an edge connecting node $u$ and node $v$.
The last line contains $m$ integers, indicating key node.

Output

Output the number of way for selecting nodes.

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

7