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.io.*;
import java.math.*;
public class Solution{
    
    static int[] a;
    static LinkedList<Integer>[] neighbers;
    static long M;
    static int d;
    
    static boolean[] tree;
    static boolean[] visited;
    
    static long valid_sets(int id,int pr){
        long rep = 1;
        for(int i:neighbers[id]){
            if(i==pr) continue;
            if(!tree[i]) continue;
            rep *= valid_sets(i,id) + 1;
            rep %= M;
        }
        return rep;
        
    }
    
    static void remplir_tree(int id,int pr,int min){
        tree[id] = true;
        
        for(int i:neighbers[id]){
            if(i==pr) continue;
            if(a[i]>min && a[i]<=min+d){
                remplir_tree(i,id,min);
            }else if(a[i]==min && !visited[i]){
                remplir_tree(i,id,min);
            }
        }
        
    }
    
    public static void main(String[] args)throws IOException{
                
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        PrintWriter out = new PrintWriter(System.out);
        
        d = Integer.parseInt(st.nextToken());
        int n = Integer.parseInt(st.nextToken());
        M = 1000000007;
        neighbers = new LinkedList[n+1];
        for(int i=1;i<=n;i++) neighbers[i] = new LinkedList<Integer>();
        a = new int[n+1];
        st = new StringTokenizer(br.readLine());
        for(int i=1;i<=n;i++){
            a[i] = Integer.parseInt(st.nextToken());
        }
        
        for(int i=1;i<n;i++){
            st = new StringTokenizer(br.readLine());
            int u = Integer.parseInt(st.nextToken());
            int v = Integer.parseInt(st.nextToken());
            neighbers[u].add(v);
            neighbers[v].add(u);
        }
        
        tree = new boolean[n+1];
        visited = new boolean[n+1];
        
        long rep = 0;
        for(int i=1;i<=n;i++){
            remplir_tree(i,-1,a[i]);
            rep += valid_sets(i,-1);
            rep %= M;
            visited[i] = true;
            Arrays.fill(tree,false);
        }
        
        out.println(rep);
        
        out.flush();
        
        
    }
    
}