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.IOException;
import java.io.UnsupportedEncodingException;
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.io.InputStream;

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

class TaskD {
    int maxn = 2200;
    static final int mod = 1000000007;

    ArrayList<Integer>[] tree = new ArrayList[maxn];
    long[] a = new long[maxn];
    long[] count = new long[maxn];
    boolean[] visited = new boolean[maxn];
    int d, n;

    public void solve(int testNumber, MyInputReader in, PrintWriter out) {
        d = in.readInt();
        n = in.readInt();
        for(int i=1; i<=n; i++) {
            a[i] = in.readInt();
            tree[i] = new ArrayList<>();
        }
        for(int i=1; i<=n-1; i++){
            int u = in.readInt();
            int v = in.readInt();
            tree[u].add(v);
            tree[v].add(u);
        }
        long result = 0;
        for(int i=1; i <= n; i++){
            for(int j=1; j<=n; j++){
                count[j] = 0;
                visited[j] = false;
            }
            visit(i, i);
            result = (result + count[i]) % mod;
        }
        out.println(result);
    }

    void visit(int node, int root){
        visited[node] = true;
        count[node] = 1;
        for(int i=0; i< tree[node].size(); i++){
            int v = tree[node].get(i);
            if(!visited[v]){
                if((a[v] < a[root] || a[v] > a[root] + d)) continue;
                if((a[v] == a[root]) && (v < root)) continue;
                visit(v, root);
                count[node] = (count[node] * (count[v] + 1))%mod;
            }
        }
    }
}

class MyInputReader {

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public MyInputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public static boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

}

