5437: Valid Sets
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
上传者：
提交：1
通过：1
题目描述
D. Valid Sets
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
As you know, an undirected connected graph with n nodes and n-1 edges is called a tree. You are given an integer d and a tree consisting of n nodes. Each node i has a value ai associated with it.
We call a set S of tree nodes valid if following conditions are satisfied:
We call a set S of tree nodes valid if following conditions are satisfied:
- S is non-empty.
- S is connected. In other words, if nodes u and v are in S, then all nodes lying on the simple path between u and v should also be presented in S.
-
.
Input
The first line contains two space-separated integers d (0≤d≤2000) and n (1≤n≤2000). The second line contains n space-separated positive integers a1,a2,...,an(1≤ai≤2000).
Then the next n-1 line each contain pair of integers u and v (1≤u,v≤n) denoting that there is an edge between u and v. It is guaranteed that these edges form a tree.
Output
Print the number of valid sets modulo 1000000007.
Examples
Input
1 4 2 1 3 2 1 2 1 3 3 4
Output
8
Input
0 3 1 2 3 1 2 2 3
Output
3
Input
4 8 7 8 7 5 4 6 4 10 1 6 1 2 5 8 1 3 3 5 6 7 3 4
Output
41
Note
In the first sample, there are exactly 8 valid sets: {1},{2},{3},{4},{1,2},{1,3},{3,4} and {1,3,4}. Set {1,2,3,4} is not valid, because the third condition isn't satisfied. Set {1,4} satisfies the third condition, but conflicts with the second condition. 输入样例 复制
输出样例 复制