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.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;
import static java.lang.Math.*;
import static java.util.Arrays.fill;

public class Main {
    private void run() {
        try {
            Locale.setDefault(Locale.US);
        } catch (Exception e) {
        }
        boolean oj = true;
        try {
            oj = System.getProperty("MYLOCAL") == null;
        } catch (Exception e) {
        }

        if (oj) {
            sc = new FastScanner(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
        } else {
            try {
                sc = new FastScanner(new FileReader("input.txt"));
                out = new PrintWriter(new FileWriter("output.txt"));
            } catch (IOException e) {
                MLE();
            }
        }
        Solver s = new Solver();
        s.sc = sc;
        s.out = out;
        s.solve();
        if (!oj) {
            err.println("Time: " + (System.currentTimeMillis() - timeBegin) / 1e3);
            err.printf("Mem: %d\n", (Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) >> 20);
        }
        out.flush();
    }

    private void show(int[] arr) {
        for (int v : arr) {
            err.print(" " + v);
        }
        err.println();
    }

    public static void exit() {
        err.println("Time: " + (System.currentTimeMillis() - timeBegin) / 1e3);
        err.printf("Mem: %d\n", (Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) >> 20);
        out.flush();
        out.close();
        System.exit(0);
    }

    public static void MLE() {
        int[][] arr = new int[1024 * 1024][];
        for (int i = 0; i < arr.length; i++) {
            arr[i] = new int[1024 * 1024];
        }
    }

    public static void main(String[] args) {
        new Main().run();
    }

    static long timeBegin = System.currentTimeMillis();
    static FastScanner sc;
    static PrintWriter out;
    static PrintStream err = System.err;
}

class FastScanner {

    BufferedReader br;
    StringTokenizer st;

    FastScanner(InputStreamReader reader) {
        br = new BufferedReader(reader);
        st = new StringTokenizer("");
    }

    String next() {
        while (!st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception ex) {
                return null;
            }
        }
        return st.nextToken();
    }

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

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        try {
            return br.readLine();
        } catch (IOException ex) {
            return null;
        }
    }
}

class Solver {
    FastScanner sc;
    PrintWriter out;
    PrintStream err = System.err;

    void myAssert(boolean OK) {
        if (!OK)
            Main.MLE();
    }

    final int mod = (int)1e9 + 7;
    int d, n;
    int[] a;
    ArrayList<Integer>[] gr;

    void solve(){
        d = sc.nextInt();
        n = sc.nextInt();
        a = new int[n+1];
        gr = new ArrayList[n+1];
        for(int v = 1; v <= n; ++v){
            a[v] = sc.nextInt();
            gr[v] = new ArrayList<Integer>(0);
        }
        for (int i = 0; i < n - 1; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            gr[a].add(b);
            gr[b].add(a);
        }
        long ans = 0;
        for( int v = 1; v <= n; ++ v )
            ans += dfs(v,-1,v);
        out.println( ans % mod );
    }

    private long dfs(int v, int p, int root) {
        long ans = 1;
        for(int to : gr[v]){
            if( to == p ) continue;
            if( (a[to] < a[root] &&  a[root]-a[to]<=d ) || (a[to]==a[root] && to < root) )
                ans = ans * (dfs(to,v,root)+1) % mod;
        }
        return ans;
    }

}