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.util.*;
public class ValidSets
{
    static ArrayList<ArrayList<Integer>> adjList = new ArrayList<ArrayList<Integer>>();
    static long VAL[] = new long [2050];
    static long  DP[] = new long [2050];
    static long ans =0, MOD = 1000000007;
    static long D;
    static int  N;
    public static void main(String[]args)
    {
        InputReader1 sc = new InputReader1(System.in);
        for(int i=0;i<=2050;i++)adjList.add(new ArrayList<Integer>());
        D = sc.nextLong() ; 
        N = sc.nextInt();
        for(int i=1;i<=N;i++)
            VAL[i] = sc.nextLong();
        for(int i=1;i<N;i++)
        {
            int u = sc.nextInt() , v = sc.nextInt();
            adjList.get(u).add(v);
            adjList.get(v).add(u);
        }
        for(int i=1;i<=N;i++)
        {
            Arrays.fill(DP,0);
            dfs(i,i,-1);
            ans += DP[i];
            ans %= MOD;
        } 
        System.out.println(ans);
    }
    static void dfs(int root , int node , int par)
    {
        DP[node] = 1;
        for(int next:adjList.get(node))
        {
            if(next==par)continue;
            if((VAL[next] < VAL[root])|| (VAL[next] > VAL[root] +D))continue;
            // Prevent overcounting
            if((VAL[next] == VAL[root] && next<root))continue;
            dfs(root,next,node);
            DP[node] = (DP[node]*(DP[next]+1)) % MOD;
        }
    }
}
class InputReader1 
{

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

    public InputReader1(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 nextInt() {
        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 & 15;
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public long nextLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c & 15;
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String next() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public String nextLine() {
        int c = read();
        //while (c != '\n' && c != '\r' && c != '\t' && c != -1)
        //c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (c != '\n' && c != '\r' && c != '\t' && c != -1);
        return res.toString();
    }

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

}   
