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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class A {
	
	static final int mod = (int)1e9 + 7;
	static int d, s, su, a[];
	static ArrayList<Integer>[] adjList;
	
	static int dfs(int u, int p)
	{
		if(a[u] < s || a[u] == s && u < su || a[u] - s > d)
			return 1;
		long ret = 1;
		for(int v: adjList[u])
			if(v != p)
			{
				ret *= dfs(v, u);
				ret %= mod;
			}
		if(u != su)
			ret = (ret + 1) % mod;
		return (int)ret;
	}
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		d = sc.nextInt();
		int n = sc.nextInt();
		a = new int[n];
		for(int i = 0; i < n; ++i)
			a[i] = sc.nextInt();
		adjList = new ArrayList[n];
		for(int i = 0; i < n; ++i)
			adjList[i] = new ArrayList<>(1);
		for(int i = 1; i < n; ++i)
		{
			int u = sc.nextInt() - 1, v = sc.nextInt() - 1;
			adjList[u].add(v);
			adjList[v].add(u);
		}
		int ans = 0;
		for(int i = 0; i < n; ++i)
		{
			s = a[su = i];
			ans += dfs(i, -1);
			ans %= mod;
		}
		out.println(ans);
		out.flush();
		out.close();
	}

	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

		public String nextLine() throws IOException {return br.readLine();}

		public double nextDouble() throws IOException { return Double.parseDouble(next()); }

		public boolean ready() throws IOException {return br.ready();} 
	}
} 