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.*;
import java.math.BigInteger;
import java.util.*;

public class Main implements Runnable {

    // leave empty to read from stdin/stdout
    private static final String TASK_NAME_FOR_IO = "";

    // file names
    private static final String FILE_IN = TASK_NAME_FOR_IO + ".in";
    private static final String FILE_OUT = TASK_NAME_FOR_IO + ".out";

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tokenizer = new StringTokenizer("");

    public static void main(String[] args) {
        new Thread(new Main()).start();
    }
    int n, d;
    List<Integer> []g;
    int []a;

    boolean []used;
    long []dp;
    final static long MOD = (long)(1e9) + 7;
    private void solve() throws IOException {
        d = nextInt();
        n = nextInt();

        g = new LinkedList[n];
        for(int i = 0; i < n; ++i) g[i] = new LinkedList<Integer>();
        a = new int[n];
        for(int i = 0; i < n; ++i) a[i] = nextInt();
        for(int i = 0; i + 1 < n; ++i) {
            int v = nextInt()-1, u = nextInt()-1;
            g[v].add(u);
            g[u].add(v);
        }

        dp = new long[n];
        used = new boolean[n];

        long ret = 0;
        for(int i = 0; i < n; ++i) {
            Arrays.fill(dp, 0);
            Arrays.fill(used, false);
            dfs(i, i);

            ret = (ret + dp[i]) % MOD;
            // System.out.println(i + " " + dp[i]);
        }
        out.println(ret);
    }

    private void dfs(int x, int root) {
        used[x] = true;
        dp[x] = 1;
        for(int i : g[x]) {
            if (used[i]) continue;
            if (a[i] < a[root] || a[i] > a[root] + d) continue;
            if (a[i] == a[root] && i < root) continue;
            dfs(i, root);
            dp[x] = dp[x] * (dp[i] + 1);
            dp[x] %= MOD;
        }
    }

    public void run() {
        long timeStart = System.currentTimeMillis();

        boolean fileIO = TASK_NAME_FOR_IO.length() > 0;
        try {

            if (fileIO) {
                in = new BufferedReader(new FileReader(FILE_IN));
                out = new PrintWriter(new FileWriter(FILE_OUT));
            } else {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(new OutputStreamWriter(System.out));
            }

            solve();

            in.close();
            out.close();
        } catch (IOException e) {
            throw new IllegalStateException(e);
        }
        long timeEnd = System.currentTimeMillis();

        if (fileIO) {
            System.out.println("Time spent: " + (timeEnd - timeStart) + " ms");
        }
    }

    private String nextToken() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null) {
                return null;
            }
            tokenizer = new StringTokenizer(line);
        }
        return tokenizer.nextToken();
    }

    private int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    private BigInteger nextBigInt() throws IOException {
        return new BigInteger(nextToken());
    }

    private long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    private double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

}