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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DValidSets solver = new DValidSets();
        solver.solve(1, in, out);
        out.close();
    }

    static class DValidSets {
        int d;
        int n;
        int[] vals;
        ArrayList<Integer>[] adjL;
        int mod = (int) 1e9 + 7;
        long[] dp;

        public void readInput(Scanner sc) {
            d = sc.nextInt();
            n = sc.nextInt();
            vals = new int[n];
            for (int i = 0; i < n; i++)
                vals[i] = sc.nextInt();
            adjL = new ArrayList[n];
            for (int i = 0; i < n; i++)
                adjL[i] = new ArrayList<>();
            for (int i = 0; i < n - 1; i++) {
                int u = sc.nextInt() - 1, v = sc.nextInt() - 1;
                adjL[u].add(v);
                adjL[v].add(u);
            }
        }

        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            int q = 1;
            while (q-- > 0) {
                readInput(sc);
                long ans = 0;
                for (int i = 0; i < n; i++) {
                    dp = new long[n];
                    dfs(i, i, i);
                    ans += dp[i];
                    ans %= mod;
                }
                pw.println(ans);
            }
        }

        private void dfs(int u, int p, int root) {
            dp[u] = 1;
            for (int v : adjL[u]) {
                if (v == p)
                    continue;
                if (vals[v] < vals[root] || vals[v] > vals[root] + d || (vals[v] == vals[root] && root > v))
                    continue;
                dfs(v, u, root);
                dp[u] *= (dp[v] + 1);
                dp[u] %= mod;
            }
        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() {
            try {
                while (st == null || !st.hasMoreTokens())
                    st = new StringTokenizer(br.readLine());
                return st.nextToken();
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }

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

    }
}

