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 D {
    public static PrintStream out = System.out;
    public static InputReader in = new InputReader(System.in);
    static long MOD = 1000000007;
    static int D, N;
    static int[] a;
    static boolean[] marked;
    static List<List<Integer>> adj;
    public static void main(String args[]) {
        D = in.nextInt();
        N = in.nextInt();
        a = new int[N];
        adj = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            a[i] = in.nextInt();
        }
        for (int i = 0; i < N; i++) {
            adj.add(new ArrayList<Integer>());
        }
        for (int i = 0; i < N - 1; i++) {
            int u = in.nextInt() - 1;
            int v = in.nextInt() - 1;
            adj.get(u).add(v);
            adj.get(v).add(u);
        }
        long tot = 0;
        marked = new boolean[N];
        for (int i = 0; i < N; i++) {
            tot += f(i, i);
            tot %= MOD;
        }
        out.println(tot);
    }
    static long f(int v, int root) {
        long ret = 1;
        marked[v] = true;
        for (int u : adj.get(v)) {
            if (!marked[u]) {
                // out.println(u + " " + root);
                if (a[u] > a[root] + D || a[u] < a[root]) continue;
                if (a[u] == a[root] && root < u) continue;
                ret *= 1 + f(u, root);
                ret %= MOD;
            }
        }
        marked[v] = false;
        // out.println(v + " " + root + " " + ret);
        return ret;
    }
}
class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
    public InputReader(InputStream stream) {
	reader = new BufferedReader(new InputStreamReader(stream), 32768);
	tokenizer = null;
    }
    public String next() {
	while (tokenizer == null || !tokenizer.hasMoreTokens()) {
	    try {
		tokenizer = new StringTokenizer(reader.readLine());
	    } catch (IOException e) {
		throw new RuntimeException(e);
	    }
	}
	return tokenizer.nextToken();
    }
    public double nextDouble() {
	return Double.parseDouble(next());
    }
    public long nextLong() {
	return Long.parseLong(next());
    }
    public int nextInt() {
	return Integer.parseInt(next());
    }
}
