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 static java.lang.System.in;

public class Main {
    static ArrayList<Integer>[] graph;
    static long mod = 1000000000+7;
    static int[] a;
    static boolean[] finish;
    static long ans = 0;
    public static void main(String[] args)throws IOException {
        Scanner sc = new Scanner(System.in);
        int d = sc.nextInt(), n = sc.nextInt();
        a = new int[n+1];
        finish = new boolean[n+1];
        graph = new ArrayList[n+1];
        for(int i=0;i<=n;i++) graph[i]=new ArrayList<>();
        for(int i=1;i<=n;i++) a[i]=sc.nextInt();
        for(int i=1;i<n;i++){
            int u = sc.nextInt(), v = sc.nextInt();
            graph[u].add(v);
            graph[v].add(u);
        }
        for(int i=1;i<=n;i++){
            HashMap<Integer,ArrayList<Integer>> g = bfs(i,d);
            ans = (ans+dfs(i,g))%mod;
        }
        // ans += n;
        System.out.println(ans);
    }
    static HashMap<Integer,ArrayList<Integer>> bfs(int s, int d){
        HashMap<Integer,ArrayList<Integer>> ans = new HashMap<>();
        HashSet<Integer> vis = new HashSet<>();
        LinkedList<Integer> que = new LinkedList<>();
        que.add(s);vis.add(s);
        while(que.size()>0){
            int cur = que.poll();
            ans.put(cur,new ArrayList<>());
            for(int w:graph[cur]){
                if(vis.add(w)&&a[w]>=a[s]&&a[w]<=a[s]+d) {
                    if(a[w]==a[s]&&w<s) continue;
                    que.add(w);
                    ans.get(cur).add(w);
                }
            }
        }
        return ans;
    }
    static long dfs(int s, HashMap<Integer,ArrayList<Integer>> g){
        if(g.get(s).size()==0) return 1;
        long res = 1;
        for(int to:g.get(s)){
            res *= 1+dfs(to,g);
            res %= mod;
        }
        return res;
    }
}
