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.Arrays;
import java.util.StringTokenizer;

public class CR277_valid_sets {

    private static final int M = 1000000007;
    private static int[][] g;
    private static boolean[] visited;
    private static int[] v;
    private static int diff;

    public static void main(String... args) throws IOException {
        MyScanner sc = new MyScanner();
        diff = sc.nextInt();
        int n = sc.nextInt();

        v = new int[n];

        for (int i = 0; i < n; i++) {
            v[i] = sc.nextInt();
        }

        int[] from = new int[n - 1];
        int[] to = new int[n - 1];

        for (int i = 0; i < n - 1; i++) {
            from[i] = sc.nextInt();
            to[i] = sc.nextInt();
        }

        g = calculateGraph(n, from, to);
        visited = new boolean[n];

        long out = 0;
        for (int i = 0; i < n; i++) {
            Arrays.fill(visited, false);
            out = (out + dfs(i, i)) % M;
        }
        System.out.println(out);
    }

    private static long dfs(int i, int min) {
        long out = 1;
        visited[i] = true;
        for (int j = 0; j < g[i].length; j++) {
            int child = g[i][j];
            if (!visited[child] && v[child] >= v[min] && v[child] - v[min] <= diff && (v[child] != v[min] || child > min)) {
                out = (out * (dfs(child, min) + 1)) % M;
            }
        }
        return out;
    }

    private static int[][] calculateGraph(int n, int[] from, int[] to) {
        int[][] g = new int[n][];
        int[] degree = calculateDegree(n, from, to);
        for (int i = 0; i < n; i++) {
            g[i] = new int[degree[i]];
        }
        Arrays.fill(degree, 0);
        for (int i = 0; i < from.length; i++) {
            int a = from[i] - 1;
            int b = to[i] - 1;
            g[a][degree[a]++] = b;
            g[b][degree[b]++] = a;
        }
        return g;
    }

    private static int[] calculateDegree(int n, int[] from, int[] to) {
        int[] degree = new int[n];
        for (int i = 0; i < from.length; i++) {
            degree[from[i] - 1]++;
            degree[to[i] - 1]++;
        }
        return degree;
    }

    static class MyScanner {

        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() throws IOException {
            if (st == null || !st.hasMoreTokens()) {
                String line = br.readLine();
                while (line.isEmpty()) {
                    line = br.readLine();
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            String next = next();
            return Integer.parseInt(next);
        }

        private long nextLong() throws IOException {
            String next = next();
            return Long.parseLong(next);
        }
    }
}
