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.
// cat test.in | (javac Main.java && java Main) > test.out

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

public class Main {
  public static void main(String[] args) {
    Scanner s = new Scanner(System.in);
    int d = s.nextInt(), n = s.nextInt();
    Node[] node = new Node[n];
    for (int i = 0; i < n; i++) {
      node[i] = new Node(s.nextInt(), i);
    }
    for (int i = 0; i < n - 1; i++) {
      int u = s.nextInt() - 1, v = s.nextInt() - 1;
      node[u].children.add(node[v]);
      node[v].children.add(node[u]);
    }
    long ans = 0;
    for (int i = 0; i < n; i++) {
      ans += node[i].count(node[i], null, d);
      ans %= MAX;
    }
    System.out.println(ans);
  }

  public static class Node {
    int value, index;
    List<Node> children;

    public Node(int value, int index) {
      this.value = value;
      this.index = index;
      children = new ArrayList<Node>();
    }

    public long count(Node root, Node parent, int d) {
      long ret = 1;
      for (Node c : children) {
        if (c != parent && c.value >= root.value && c.value <= root.value + d
            && (c.value != root.value || c.index < root.index)) {
          ret *= (c.count(root, this, d) + 1);
          ret %= MAX;
        }
      }
      return ret;
    }
  }

  public static final long MAX = 1000000007;
}
