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.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

public class SolverD {

	public static void main(String[] Args) throws NumberFormatException,
			IOException {
		new SolverD().Run();
	}

	PrintWriter pw;
	StringTokenizer Stok;
	BufferedReader br;

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

	public int nextInt() throws NumberFormatException, IOException {
		return Integer.parseInt(nextToken());
	}

	public double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(nextToken());
	}

	public long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(nextToken());
	}

	final long del=(long)1e9+7;
	
	int d, n;
	List<List<Integer>> edges;
	int[] vals;
	long result=0;
	boolean[] isUsed;
	
	long goDFS(int curVert, int ans, int minVal, int maxVal){
		if (vals[curVert]<minVal)
			return 1;
		if (vals[curVert]>maxVal)
			return 1;
		
		if (vals[curVert]==minVal && isUsed[curVert])
			return 1;
		
		long result=1;
		for (Integer next : edges.get(curVert)){
			if (next!=ans){
				result=(result*goDFS(next, curVert, minVal, maxVal))%del;
			}
		}
		result++;
		return result;
		
	}
	
	public void Run() throws NumberFormatException, IOException {
		//br = new BufferedReader(new FileReader("input.txt")); pw = new PrintWriter("output.txt");
		br=new BufferedReader(new InputStreamReader(System.in));  pw=new PrintWriter(new OutputStreamWriter(System.out));
		d=nextInt();
		n=nextInt();
		edges=new ArrayList<List<Integer>>();
		vals=new int[n];
		isUsed=new boolean[n];
		for (int i=0; i<n; i++){
			edges.add(new ArrayList<Integer>());
			vals[i]=nextInt();
		}
		for (int i=0; i<n-1; i++){
			int zn1=nextInt()-1;
			int zn2=nextInt()-1;
			edges.get(zn1).add(zn2);
			edges.get(zn2).add(zn1);
		}
		
		for (int i=0; i<n; i++){
			result+=(goDFS(i,-1,vals[i],vals[i]+d)-1);
			result%=del;
			isUsed[i]=true;
		}
		pw.println(result);
		pw.flush();
		pw.close();
	}

}