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 Abood2B {
	
	static final long MOD = (long) 1e9 + 7;
	static int d, n, val[];
	static ArrayList<Integer>[] Tree;
	
	
	static long solve(int u, int p, int idx) {
		long ans = 1;
		for (int i = 0; i < Tree[u].size(); i++) {
			int v = Tree[u].get(i);
			
			if(v != p && (val[v] > val[idx] && val[v] <= val[idx] + d || val[v] == val[idx] && v > idx)) {
				ans *= (solve(v, u, idx) + 1);
				ans %= MOD;
			}
		}
		
		return ans;
	}


	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		d = sc.nextInt();
		n = sc.nextInt();
		
		val = new int[n];
		
		Tree = new ArrayList[n];
		
		for (int i = 0; i < n; i++) {
			val[i] = sc.nextInt();
			Tree[i] = new ArrayList<>();
		}
		
		for (int i = 0; i < n - 1; i++) {
			int f = sc.nextInt() - 1;
			int t = sc.nextInt() - 1;
			
			Tree[f].add(t);
			Tree[t].add(f);
		}
		
		long ans = 0;
		
		for (int i = 0; i < n; i++) {
			ans += solve(i, -1, i);
			ans %= MOD;
		}
		
		out.println(ans);
		
		out.flush();
		out.close();
	}
	
	static long q(long x) {
		return x * x * x;
	}




	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
		{
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if(x.charAt(0) == '-')
			{
				neg = true;
				start++;
			}
			for(int i = start; i < x.length(); i++)
				if(x.charAt(i) == '.')
				{
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				}
				else
				{
					sb.append(x.charAt(i));
					if(dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg?-1:1);
		}

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



	}

}