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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.LinkedList;
import java.util.List;
import java.util.StringTokenizer;

public class main {
    
    static int d, n;
    static long MOD = 1000000007;
    
    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        StringBuilder out = new StringBuilder();
        d = Reader.nextInt();
        n = Reader.nextInt();
        Graph g = new Graph(n);
        for(int i = 1; i <= n; i++)
            g.va[i].a = Reader.nextInt();
        for(int i = 1; i < n; i++)
            g.addEdge(Reader.nextInt(), Reader.nextInt());
        long res = 0;
        for(int i = 1; i <= n; i++)
            res = (res + calc(g.va[i], g.va[i].a, i, null)) % MOD;
        out.append(res).append('\n');
        PrintWriter pw = new PrintWriter(System.out);
        pw.print(out);
        pw.close();
    }
    
    static long calc(Vertex v, int min, int index, Vertex p) {
        long cur = 1;
        for(Vertex c : v.edges)
            if(c != p && ((c.a > min && c.a <= min + d) || (c.a == min && c.index > index)))
                cur = (cur * (calc(c, min, index, v) + 1)) % MOD;
        return cur;
    }
    
}

class Vertex {
    
    int index, a;
    List<Vertex> edges;
    
    public Vertex(int i) {
        index = i;
        edges = new LinkedList<Vertex>();
    }
    
}

class Graph {
    
    Vertex[] va;
    
    public Graph(int size) {
        va = new Vertex[size + 1];
        for(int i = 1; i <= size; i++)
            va[i] = new Vertex(i);
    }
    
    public void addEdge(int v1, int v2) {
        va[v1].edges.add(va[v2]);
        va[v2].edges.add(va[v1]);
    }
    
}

class Reader {
    
    public static BufferedReader reader;
    public static StringTokenizer tokenizer;
    
    public static void init(InputStream input) {
        reader = new BufferedReader(new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }
    
    public static void init(String url) throws FileNotFoundException {
        reader = new BufferedReader(new FileReader(url));
        tokenizer = new StringTokenizer("");
    }
    
    public static String next() throws IOException {
        while(!tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(reader.readLine());
        return tokenizer.nextToken();
    }
    
    public static String nextLine() throws IOException {
        return reader.readLine();
    }
    
    public static byte nextByte() throws IOException {
        return Byte.parseByte(next());
    }
    
    public static short nextShort() throws IOException {
        return Short.parseShort(next());
    }
    
    public static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    
    public static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    
    public static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    
}
