|시간 제한||메모리 제한||제출||정답||맞은 사람||정답 비율|
|5 초||512 MB||0||0||0||0.000%|
Bobo has a tree with $n$ vertices. There are $m$ vertices on the tree that bobo thinks very special.
bobo would like to choose a (maybe empty) subset of vertices as control points, so that every special vertex can reach an control points via no more than $r$ edges.
Find out the number of such subsets, modulo $(10^9 + 7)$.
The first line contains $3$ integers $n, m, r$ ($1 \leq n \leq 2000, 0 \leq m \leq n, 0 \leq r < n$).
Vertices are numbered by $1, 2, \dots, n$ for convenience.
The second line contains $m$ distinct integers $v_1, v_2, \dots, v_m$ which denotes the special vertices ($1 \leq v_i \leq n$).
Each of the following $(n - 1)$ lines contains $2$ integers $a_i, b_i$ which denotes an edge between vertices $a_i$ and $b_i$ ($1 \leq a_i, b_i \leq n$).
A single integer denotes the number of subsets.
3 1 1 1 1 2 2 3
4 1 2 1 1 2 2 3 2 4