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:

  1. S is non-empty.
  2. 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.
  3. <image>.



Your task is to count the number of valid sets. Since the result can be very large, you must print its remainder modulo 1000000007 (109 + 7).

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.
import java.util.*;
import java.io.*;
public class Main {
static ArrayList<Integer>list[];
static int visited[];
static int array[];
static long mod = (long)1E9 + 7;	
public static void main(String [] args)throws Exception{
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	StringTokenizer st = new StringTokenizer(br.readLine());
	
	int d = Integer.parseInt(st.nextToken());
	int n = Integer.parseInt(st.nextToken());
	st = new StringTokenizer(br.readLine());
	visited = new int[n];
	Arrays.fill(visited,-1);
	array = new int[n];
	for(int i = 0;i < n;i++)
		array[i] = Integer.parseInt(st.nextToken());
    
    list = new ArrayList[n];
    for(int i = 0;i < n;i++)
    	list[i] = new ArrayList<Integer>();
    
    for(int i = 0;i < n - 1;i++){
    	st = new StringTokenizer(br.readLine());
    	int u = Integer.parseInt(st.nextToken()) - 1;
    	int v = Integer.parseInt(st.nextToken()) - 1;
    	list[u].add(v);
    	list[v].add(u);
    }
    long ans = 0;
    for(int i = 0;i < n;i++){
    	ans = (ans + dfs(i,i,d)) % mod;
    }
    System.out.println(ans);			
}
static long dfs (int curr,int root,int d){
	visited[curr] = root;
	long cur = 1;
	for(int next : list[curr]){
		if(visited[next] == root)continue;
		if(array[next] < array[root]|| array[next] > array[root] + d)continue;
		if(array[next] == array[root] && next < root)continue;
		cur = (cur * (dfs(next,root,d) + 1)) % mod;
	}
	return cur;
}
}