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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.StringTokenizer;

public class ValidSets {
    private static final long MOD = 1000000007;

    private static ArrayList<ArrayList<Integer>> tree;
    private static HashSet<Integer> set;
    private static boolean[] visited;

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;

        st = new StringTokenizer(br.readLine());
        int d = Integer.parseInt(st.nextToken()), n = Integer.parseInt(st.nextToken());
        tree = new ArrayList<>(n);
        ArrayList<Vertex> vertices = new ArrayList<>(n);
        st = new StringTokenizer(br.readLine());
        for (int i = 0; i < n; i++) {
            vertices.add(new Vertex(i, Integer.parseInt(st.nextToken())));
            tree.add(new ArrayList<>());
        }
        for (int i = 0; i < n - 1; i++) {
            st = new StringTokenizer(br.readLine());
            int u = Integer.parseInt(st.nextToken()) - 1, v = Integer.parseInt(st.nextToken()) - 1;
            tree.get(u).add(v);
            tree.get(v).add(u);
        }
        vertices.sort((v1, v2) -> {
            if (v1.a == v2.a) {
                return v1.v - v2.v;
            }
            return v1.a - v2.a;
        });

        long count = n;
        for (int i = 0; i < n; i++) {
            Vertex vI = vertices.get(i);
            set = new HashSet<>();
            visited = new boolean[n];
            for (int j = i; j < n; j++) {
                Vertex vJ = vertices.get(j);
                if (vJ.a - vI.a <= d) {
                    set.add(vJ.v);
                }
            }
            count += countSubTrees(vI.v) - 1;
            count = count < 0 ? count + MOD : count % MOD;
        }
        System.out.println(count);
    }

    private static long countSubTrees(int v) {
        visited[v] = true;
        long count = 1;
        for (int u : tree.get(v)) {
            if (set.contains(u) && !visited[u]) {
                long temp = (1 + countSubTrees(u)) % MOD;
                count *= temp;
                count %= MOD;
            }
        }
        return count;
    }

    private static class Vertex {
        int v;
        int a;

        public Vertex(int v, int a) {
            this.v = v;
            this.a = a;
        }
    }
}
