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.*;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main {

  private int[] a;
  private ArrayList<ArrayList<Integer>> g;
  private int m;
  private int d;

  public static void main(String[] args) {
    try (InputReader in = new InputReader(System.in);
         PrintWriter out = new PrintWriter(System.out)) {
      new Main().run(in, out);
    }
  }

  private void run(InputReader in, PrintWriter out) {
    m = (int) 1e9 + 7;
    d = in.nextInt();
    int n = in.nextInt();
    a = new int[n];
    for (int i = 0; i < n; i++) {
      a[i] = in.nextInt();
    }
    g = new ArrayList<>(n);
    for (int i = 0; i < n; i++) {
      g.add(new ArrayList<Integer>());
    }
    for (int i = 0; i < n - 1; i++) {
      int v = in.nextInt() - 1, u = in.nextInt() - 1;
      g.get(v).add(u);
      g.get(u).add(v);
    }
    long r = 0;
    for (int i = 0; i < n; i++) {
      r = (r + f(i, i, -1)) % m;
    }
    out.print(r);
  }

  private long f(int root, int v, int p) {
    long r = 1;
    for (int u : g.get(v)) {
      if (u == p) continue;
      if (a[root] > a[u]) continue;
      if (a[root] == a[u] && u < root) continue;
      if (a[u] - a[root] <= d) {
        r = r * (f(root, u, v) + 1) % m;
      }
    }
    return r;
  }

  private long dfs(ArrayList<ArrayList<Integer>> g, int v, boolean[] used) {
    used[v] = true;
    long r = 1;
    for (int u : g.get(v)) {
      if (used[u]) continue;
      r *= dfs(g, u, used) + 1;
    }
    return r;
  }

  private static class InputReader implements AutoCloseable {

    private final BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader(InputStream in) {
      reader = new BufferedReader(new InputStreamReader(in));
    }

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

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

    @Override
    public void close() {
      try {
        reader.close();
      } catch (IOException e) {
        throw new RuntimeException(e);
      }
    }
  }
}
