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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class validsets
{
	static ArrayList<Integer> adj[];
	static int visited[], data[];
	static int n, d;
	static final int MOD = 1000000007;
	public static void main(String[] args)
	{
		FastScanner in = new FastScanner();
		d = in.nextInt();
		n = in.nextInt();
		adj = new ArrayList[n];
		data = new int[n];
		visited = new int[n];
		for(int i = 0; i < n; i++)
		{
			data[i] = in.nextInt();
			adj[i] = new ArrayList<>();
		}
		
		for(int i = 0; i < n-1; i++)
		{
			int v1 = in.nextInt()-1;
			int v2 = in.nextInt()-1;
			
			adj[v1].add(v2);
			adj[v2].add(v1);
		}
		
		long ans = 0;
		for(int i = 0; i < n; i++)
		{
			int cnt = bfs(i, data[i]);
			ans = (ans + dfs(i)) % MOD;
		}
		System.out.println(ans);
	}
	
	private static long dfs(int i)
	{
		long ret = 1;
		visited[i] = 2;
		
		for(int j : adj[i])
		{
			if(visited[j] != 1) continue;
			ret = (ret * (dfs(j)+1)) % MOD;
		}
		
		return ret;
	}

	private static int bfs(int i, int min)
	{
		Arrays.fill(visited, 0);
		ArrayDeque<Integer> q = new ArrayDeque<>();
		visited[i] = 1;
		q.add(i);
		int ret = 1;
		
		while(!q.isEmpty())
		{
			int u = q.poll();
			
			for(int v : adj[u])
			{
				if(visited[v] == 1 || data[v] > d + min || data[v] < min) continue;
				if(data[v] == min && v < i) continue;
				
				ret++;
				visited[v] = 1;
				q.add(v);
			}
		}
		
		return ret;
	}

	public static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(String s)
		{
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}

		public FastScanner()
		{
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String nextToken()
		{
			while (st == null || !st.hasMoreElements())
			{
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt()
		{
			return Integer.parseInt(nextToken());
		}

		long nextLong()
		{
			return Long.parseLong(nextToken());
		}

		double nextDouble()
		{
			return Double.parseDouble(nextToken());
		}
		
		String next()
		{
			return nextToken();
		}
	}
}
