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.io.*;
import java.util.*;

public class vs
{
	static long [] dp;
	static LinkedList<Integer> [] graph;
	static long [] a;
	static int d;
	static int n;
	static long mod = (int)1e9+7;
	static boolean [] visited;
	
	void  rec(int u, int root)
	{
		visited[u] = true;
		dp[u] = 1;
		for (int v: graph[u])
		{
			if (!visited[v])
			{
				if (a[v] < a[root] || a[v] > a[root]+d)	continue;
				if (a[v] == a[root]  && v < root)	continue;
				
				rec(v, root);
				dp[u] = ((dp[u]%mod)*((dp[v]+1)%mod))%mod;
			}
		}
		
	}

	public static void main(String args[])throws IOException
	{
		InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader sc = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
		vs vss = new vs();
        
        d = sc.nextInt();
        n = sc.nextInt();
        
        dp = new long [n+1];
        a = new long [n+1];
        visited = new boolean [n+1];
        
        for (int i = 1; i<=n; i++)
        	a[i] = sc.nextLong();
        graph = new LinkedList[n+1];
        for (int i = 1; i<= n; i++)
        	graph[i] = new LinkedList<Integer>();
        
        for (int i = 0; i<n-1; i++)
        {
        	int u = sc.nextInt();
        	int v = sc.nextInt();
        	graph[u].add(v);
        	graph[v].add(u);
        }
        long ans = 0;
        for (int i = 1; i<= n; i++)
        {
        	Arrays.fill(dp, 0);
        	Arrays.fill(visited, false);
        	vss.rec(i, i);
        	ans = (ans%mod + dp[i]%mod)%mod;
        }
        out.println(ans);
        
        
		out.close();
		out.flush();
	}
	
  static class InputReader {
	        public BufferedReader reader;
	        public StringTokenizer tokenizer;

	        public InputReader(InputStream stream) {
	            reader = new BufferedReader(new InputStreamReader(stream), 32768);
	            tokenizer = null;
	        }

	        public String next() {
	            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
	                try {
	                    tokenizer = new StringTokenizer(reader.readLine());
	                } catch (IOException e) {
	                    throw new RuntimeException(e);
	                }
	            }
	            return tokenizer.nextToken();
	        }

	        public int nextInt() {
	            return Integer.parseInt(next());
	        }

	        public long nextLong() {
	            return Long.parseLong(next());
	        }
	    }
	
}