Hongjun and the Possible Sets

There is a tree with $N$ vertices. Vertex $i$ carries a weight $a(i)$. Given one integer $d$, a set $S$ of tree vertices is a "possible set" when it satisfies all of the following conditions.

1. $S$ is not empty.
2. The vertices in $S$ are connected. That is, for any two vertices $u$ and $v$ in $S$, every vertex on the path joining them belongs to $S$.
3. $\max_{u \in S} a(u) - \min_{v \in S} a(v) \le d$

Write a program that counts the possible sets $S$. The count can be very large, so print it modulo $10^9+7$.

The first line contains $d$ and $N$. ($0 \le d \le 20000$, $1 \le N \le 20000$)

The second line contains $N$ integers, $a(1)$ through $a(N)$ in order. ($1 \le a(i) \le 20000$)

Each of the next $N-1$ lines contains two integers $u$ and $v$, an edge of the tree. ($1 \le u, v \le N$)

Print the number of possible sets modulo $10^9+7$ on the first line.

In the first example the eight possible sets are {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {3, 4} and {1, 3, 4}.