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.*;

public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().run(in, out);
        out.close();
    }

    public static int mod = 1_000_000_007;

    int N;
    List<Integer>[] adj;
    int[] a;
    int D;
    void run(FastScanner in, PrintWriter out) {

        D = in.nextInt();
        N = in.nextInt();
        a = new int[N+1];
        adj = new List[N+1];
        for (int i = 0; i < adj.length; i++) adj[i] = new ArrayList<>();

        for (int i = 1; i <= N; i++) a[i] = in.nextInt();

        for (int i = 0; i < N-1; i++) {
            int u = in.nextInt();
            int v = in.nextInt();
            adj[u].add(v);
            adj[v].add(u);
        }


        long cnt = 0;
        for (int i = 1; i <= N; i++) {
            // System.out.println(i + " " + a[i] + " " + (dfs(i, -1, a[i])));
            cnt = (cnt + dfs(i, -1, a[i], i))%mod;
        }
        out.println(cnt);
    }

    long dfs(int u, int p, int max, int maxu) {
        if (a[u] > max || max-a[u] > D) return 0;
        if (a[u] == max && u < maxu) return 0;

        long r = 1;
        for (int v : adj[u]) {
            if (v == p) continue;
            long c = dfs(v, u, max, maxu);
            r = (r * (c+1))%mod;
        }
        return r;
    }




    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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