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.math.*;
import java.io.*;
import java.text.DecimalFormat;
import java.math.BigInteger;
public class Main{
    static int d;
    static int mod=1000000007 ;
    static int[] a;
    static  ArrayList<ArrayList<Integer>> arr;
    public static void main(String[] args)  throws IOException {
        s.init(System.in);        
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n;
        d=s.ni();
        n=s.ni();
        a=new int[n];
        arr=new ArrayList<ArrayList<Integer>>();
        for(int i=0;i<n;i++){
            a[i]=s.ni();
            arr.add(new ArrayList<Integer>());
        }
        

        for(int i=0;i<n-1;i++){
            int u=s.ni()-1;
            int v=s.ni()-1;
            arr.get(u).add(v);
            arr.get(v).add(u);

        }
        long ans=0;
       
        for(int i=0;i<n;i++){
            ans+=dfs(i,-1,i)-1+mod;
            ans%=mod;
        }
        out.println(ans);
        out.close();
    }
       


   
    public static long dfs(int c,int p,int min){
        if(a[c]<a[min]) return 1;
        if(a[c]>a[min]+d) return 1;
        if(a[c]==a[min] && c<min)return 1;

        long res=1;
        for(int x:arr.get(c)){
            if(x!=p){
                
                res*= dfs(x,c,min);
                res%=mod;
            }
        }
        return res+1;

    }
    public static int gcd(int a,int b){
        if(a%b==0)
            return b;
        else
            return gcd(b,a%b);
    }
        public static class s {
        static BufferedReader reader;
        static StringTokenizer tokenizer;
 
        /** call this method to initialize reader for InputStream */
        static void init(InputStream input) {
            reader = new BufferedReader(
                        new InputStreamReader(input) );
            tokenizer = new StringTokenizer("");
        }   
 
        /** get next word */
        static String ns() throws IOException {
            while ( ! tokenizer.hasMoreTokens() ) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer(
                    reader.readLine() );
            }
            return tokenizer.nextToken();
        }
 
        static int ni() throws IOException {
            return Integer.parseInt( ns() );
        }
    
        static double nd() throws IOException {
            return Double.parseDouble( ns() );
        }
        static long nl() throws IOException {
            return Long.parseLong( ns() );
        }
        
    }
} 