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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

public class ProblemD {
    BufferedReader rd;

    private ProblemD() throws IOException {
        rd = new BufferedReader(new InputStreamReader(System.in));
        compute();
    }

    private void compute() throws IOException {
        int[] a = intarr();
        int d = a[0];
        int n = a[1];
        a = intarr();
        for(int i=0;i<a.length;i++) {
            a[i] *= 10000;
            a[i] += i+1;
        }
        d = d*10000 + 4999;
        List<List<Integer>> e = new ArrayList<>();
        for(int i=0;i<n;i++) {
            e.add(new ArrayList<Integer>());
        }
        for(int i=0;i<n-1;i++) {
            int[] uv = intarr();
            uv[0]--;
            uv[1]--;
            e.get(uv[0]).add(uv[1]);
            e.get(uv[1]).add(uv[0]);
        }

        final long B = 1000000007L;
        long res = 0;

        for(int i=0;i<n;i++) {
            int mc = a[i];
            int mx = a[i] + d;
            boolean[] visited = new boolean[n];
            visited[i] = true;
            int[] q = new int[n*2];
            int head = 0;
            int tail = 0;
            q[tail++] = i;
            while(head != tail) {
                int u = q[head++];
                for(Integer v: e.get(u)) {
                    if(!visited[v]) {
                        visited[v] = true;
                        if(a[v] >= mc && a[v] <= mx) {
                            q[tail++] = v;
                        }
                    }
                }
            }
            long[] c = new long[n];
            boolean[] vt = new boolean[n];
            for(int j=tail-1;j>=0;j--) {
                int u = q[j];
                vt[u] = true;
                boolean found = false;
                long x = 1;
                for(Integer v: e.get(u)) {
                    if(vt[v]) {
                        found = true;
                        long p = c[v];
                        p++;
                        p %= B;
                        x *= p;
                        x %= B;
                    }
                }
                if(found) {
                    c[u] = x;
                    c[u] %= B;
                } else {
                    c[u] = 1;
                }
            }
            res += c[i];
            res %= B;
        }
        out(res);
    }

    private int pint() throws IOException {
        return pint(rd.readLine());
    }

    private int pint(String s) {
        return Integer.parseInt(s);
    }



    private int[] intarr() throws IOException {
        return intarr(rd.readLine());
    }

    private int[] intarr(String s) {
        String[] q = s.split(" ");
        int n = q.length;
        int[] a = new int[n];
        for(int i=0;i<n;i++) {
            a[i] = Integer.parseInt(q[i]);
        }
        return a;
    }



    private long plong() throws IOException {
        return plong(rd.readLine());
    }

    private long plong(String s) {
        return Long.parseLong(s);
    }



    private long[] longarr() throws IOException {
        return longarr(rd.readLine());
    }

    private long[] longarr(String s) {
        String[] q = s.split(" ");
        int n = q.length;
        long[] a = new long[n];
        for(int i=0;i<n;i++) {
            a[i] = Long.parseLong(q[i]);
        }
        return a;
    }

    private static void out(Object x) {
        System.out.println(x);
    }

    public static void main(String[] args) throws IOException {
        new ProblemD();
    }
}
