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.Arrays;

import static java.lang.Integer.parseInt;

/**
 * ToDo: describe
 *
 * @author keks
 */
public class D277 {
    private static final int MOD = 1000000007;

    public static void main(String[] args) throws IOException {
        final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        String st = reader.readLine();
        String[] split = st.split("\\s");
        final int d = parseInt(split[0]);
        final int n = parseInt(split[1]);

        st = reader.readLine();
        split = st.split("\\s");
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = parseInt(split[i]);
        }

        final ArrayList<Integer>[] graph = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            graph[i] = new ArrayList<>();
        }

        for (int i = 0; i < n - 1; i++) {
            st = reader.readLine();
            split = st.split("\\s");
            final int u = parseInt(split[0]);
            final int v = parseInt(split[1]);
            graph[u - 1].add(v - 1);
            graph[v - 1].add(u - 1);
        }

        final boolean[] vis = new boolean[n];
        long count = 0;
        for (int i = 0; i < n; i++) {
            Arrays.fill(vis, false);
            count = (count + dfs(graph, vis, a, i, a[i], i, d)) % MOD;
        }
        System.out.println(count);
    }

    private static long dfs(ArrayList<Integer>[] graph, boolean[] vis, int[] a, int u, int min, int root, int d) {
        long count = 1;
        vis[u] = true;
        for (Object rv : graph[u]) {
            if (rv instanceof Integer) {
                Integer v = (Integer) rv;
                if (vis[v] || a[v] < min || a[v] - d > min || (a[v] == min && v > root)) continue;

                count = (count * (dfs(graph, vis, a, v, min, root, d) + 1)) % MOD;
            }
        }

        return count;
    }
}
