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.lang.*;
import java.math.*;
import java.io.*;

/* spar5h */

public class cf1 implements Runnable{    
	
	static class pair {
		
		int i, w;
		
		pair(int i, int w) {
			this.i = i; this.w = w;
		}
	}
	
	static class comp implements Comparator<pair> {
		
		public int compare(pair x, pair y) {
			
			if(x.w < y.w)
				return -1;
			
			if(x.w > y.w)
				return 1;
			
			return 0;
		}
	}
	
	final static long mod = (long)1e9 + 7; 
	
	static ArrayList<Integer>[] adj;
	static int vis[], check[], a[];
	static long dp[];
	
	static void dfs(int x, int d) {
		
		vis[x] = 1; dp[x] = 1;
		
		for(int i = 0; i < adj[x].size(); i++) {
			
			int y = adj[x].get(i);
			
			if(check[y] == 0 && vis[y] == 0 && a[y] <= d) {
				dfs(y, d); dp[x] = (dp[x] * dp[y]) % mod;
			}
		}
		
		dp[x] = (dp[x] + 1) % mod;
	}
	
	public void run() {

		InputReader s = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);
		
		int d = s.nextInt(), n = s.nextInt();
		
		ArrayList<pair> list = new ArrayList<pair>();
		
		a = new int[n + 1];
		
		for(int i = 1; i <= n; i++)
			a[i] = s.nextInt();
		
		for(int i = 0; i < n; i++)
			list.add(new pair(i + 1, a[i + 1]));
		
		Collections.sort(list, new comp());
		
		adj = new ArrayList[n + 1];
		
		for(int i = 1; i <= n; i++)
			adj[i] = new ArrayList<Integer>();
		
		for(int i = 0; i < n - 1; i++) {
			
			int u = s.nextInt(), v = s.nextInt();
			adj[u].add(v); adj[v].add(u);
		}
		
		check = new int[n + 1];
		
		long res = 0;
		
		for(int i = 0; i < list.size(); i++) {
			
			vis = new int[n + 1];
			dp = new long[n + 1];
			
			dfs(list.get(i).i, list.get(i).w + d);
			
			res = (res + dp[list.get(i).i]) % mod;
			res = (res + mod - 1) % mod;
			
			check[list.get(i).i] = 1;
		}
		
		w.println(res);
		
		w.close();
	}
	
	static class InputReader {
		
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		
		public InputReader(InputStream stream)
		{
			this.stream = stream;
		}
		
		public int read()
		{
			if (numChars==-1) 
				throw new InputMismatchException();
			
			if (curChar >= numChars)
			{
				curChar = 0;
				try 
				{
					numChars = stream.read(buf);
				}
				catch (IOException e)
				{
					throw new InputMismatchException();
				}
				
				if(numChars <= 0)				
					return -1;
			}
			return buf[curChar++];
		}
	 
		public String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
		}
		public int nextInt()
		{
			int c = read();
			
			while(isSpaceChar(c)) 
				c = read();
			
			int sgn = 1;
			
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			
			int res = 0;
			do 
			{
				if(c<'0'||c>'9') 
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c)); 
			
			return res * sgn;
		}
		
		public long nextLong() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			long res = 0;
			
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c));
				return res * sgn;
		}
		
		public double nextDouble() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') 
			{
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') 
			{
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
		
		public String readString() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(c));
			
			return res.toString();
		}
	 
		public boolean isSpaceChar(int c) 
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	 
		public String next() 
		{
			return readString();
		}
		
		public interface SpaceCharFilter 
		{
			public boolean isSpaceChar(int ch);
		}
	}
    
	public static void main(String args[]) throws Exception
	{
		new Thread(null, new cf1(),"cf1",1<<26).start();
	}
}   