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.
/**
 * ******* Created  on 10/12/19 8:24 PM*******
 */

import java.io.*;
import java.util.*;

public class D486 implements Runnable {

    private static final int MAX = (int) (1E5 + 5);
    private static final int MOD = (int) (1E9 + 7);
    private static final int Inf = (int) (1E9 + 10);
    List<Integer>[] adj = new List[2005];
    int[] a = new int[2005];
    int d;
    private void solve() throws IOException {
        d = reader.nextInt();
        int n = reader.nextInt();


        for(int i =1;i<=n;i++)
            a[i] = reader.nextInt();
        for(int i=1;i<=n;i++)
            adj[i] = new ArrayList<>();
        for(int i = 0;i+1<n;i++){
            int x = reader.nextInt();
            int y = reader.nextInt();
            adj[x].add(y);
            adj[y].add(x);
        }

        long res = 0;
        for(int i =1;i<=n;i++){
            res = (res + fun(i,0,i))%MOD;
        }
        writer.println(res);
    }

    private long fun(int v, int p, int r) {
        if(a[r] < a[v] || a[r] == a[v] && v <r || a[r] -a[v] >d)
            return 0;
        long res = 1;
        for(int u : adj[v]){
            if(u != p){
                res = (res * (1+ fun(u,v,r)) )%MOD;
            }
        }
        return res;
    }

    public static void main(String[] args) throws IOException {
        try (Input reader = new StandardInput(); PrintWriter writer = new PrintWriter(System.out)) {
            new D486().run();
        }
    }

    StandardInput reader;
    PrintWriter writer;

    @Override
    public void run() {
        try {
            reader = new StandardInput();
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    interface Input extends Closeable {
        String next() throws IOException;

        default int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        default long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        default double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        default int[] readIntArray() throws IOException {
            return readIntArray(nextInt());
        }

        default int[] readIntArray(int size) throws IOException {
            int[] array = new int[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        default long[] readLongArray(int size) throws IOException {
            long[] array = new long[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextLong();
            }
            return array;
        }
    }

    private static class StandardInput implements Input {
        private final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        private StringTokenizer stringTokenizer;

        @Override
        public void close() throws IOException {
            reader.close();
        }

        @Override
        public String next() throws IOException {
            if (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                stringTokenizer = new StringTokenizer(reader.readLine());
            }
            return stringTokenizer.nextToken();
        }
    }
}
