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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;


public class Main {

    private static void dfs(int u, int val, int c, List<List<Node>> G, int[] v, int d, long[] dp) {
        v[u]=1;
        dp[u]=1;
        for( Node node : G.get(u)) {
            if(node.c < val || node.c-val > d || (node.c==val && node.v < c)) continue;
            if(v[node.v]==1) continue;
            dfs(node.v,val,c,G,v,d,dp);
            dp[u] = 1l*(dp[node.v]+1)*dp[u]%1000000007; 
        }
    }

    

    static class Node {
    
        int c;
        int v;
        public Node(int v, int c) {
            this.v=v;this.c=c;
        }
    }
    
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        
        String[] in = br.readLine().split(" ");
        
        int d = Integer.parseInt(in[0]);
        int n = Integer.parseInt(in[1]);
        ArrayList<int[]> A = new ArrayList<>();
        in=br.readLine().split(" ");
        List<List<Node>> G = new ArrayList<>();
        for(int i=0;i<n;i++) {
            int[] tmp = new int[2];
            tmp[0]=i;
            tmp[1]=Integer.parseInt(in[i]);
            A.add(tmp);
            G.add(new ArrayList<Node>());
        }
        for(int i=0;i<n-1;i++) {
            in=br.readLine().split(" ");
            int u = Integer.parseInt(in[0]);
            int v = Integer.parseInt(in[1]);
            u--;v--;
            Node tmp1 = new Node(u, A.get(u)[1]);
            Node tmp2 = new Node(v, A.get(v)[1]);
            G.get(u).add(tmp2);
            G.get(v).add(tmp1);
        }
        
        int mod = 1000000007;
        long ans = 0;
        for(int i=0;i<n;i++){
            int[] v = new int[n];
            long[] dp = new long[n];
            dfs(A.get(i)[0], A.get(i)[1],A.get(i)[0], G,v,d,dp);
            ans = ans + 1l*dp[A.get(i)[0]];
            ans %= mod;
        }
        
        bw.append(ans+"\n");
        bw.close();
        
        
    }


}
