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.
//package codeforces;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class D {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter writer = new PrintWriter(System.out);
    StringTokenizer stringTokenizer;

    String next() throws IOException {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(reader.readLine());
        }
        return stringTokenizer.nextToken();
    }

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

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

    final int MOD = 1000 * 1000 * 1000 + 7;
    int sum(int a, int b) {
        a += b;
        return a >= MOD ? a - MOD : a;
    }

    @SuppressWarnings("unchecked")
    void solve() throws IOException {
        final int d = nextInt();
        final int n = nextInt();
        final int[] a = new int[n + 1];
        class Vertex {
            int id, a;

            Vertex(int id, int a) {
                this.id = id;
                this.a = a;
            }
        }
        final Vertex[] vertices = new Vertex[n];
        for(int i = 0; i < n; i++) {
            final int x = nextInt();
            vertices[i] = new Vertex(i + 1, x);
            a[i + 1] = x;
        }
        Arrays.sort(vertices, new Comparator<Vertex>() {
            @Override
            public int compare(Vertex o1, Vertex o2) {
                return o1.a - o2.a;
            }
        });
        final List<List<Integer>> g = new ArrayList<>();
        for(int i = 0; i <= n; i++) {
            g.add(new ArrayList<Integer>());
        }
        for(int i = 1; i < n; i++) {
            int u = nextInt();
            int v = nextInt();
            g.get(u).add(v);
            g.get(v).add(u);
        }
        final boolean[] used = new boolean[n + 1];
        class Utils {
            final int MOD = 1000 * 1000 * 1000 + 7;
            int sum(int a, int b) {
                a += b;
                return a >= MOD ? a - MOD : a;
            }
            int product(int a, int b) {
                return (int)(1l * a * b % MOD);
            }
            int countTrees(int u, int parent, int root) {
                int result = 1;
                for (int v : g.get(u)) {
                    if(!used[v] && a[v] >= a[root] && a[v] <= a[root] + d && v != parent) {
                        result = product(result, 1 + countTrees(v, u, root));
                    }
                }
                return result;
            }
        }
        Utils utils = new Utils();
        int ans = 0;
        for(int i = 0; i < n; i++) {
            final int id = vertices[i].id;
            ans = utils.sum(ans, utils.countTrees(id, 0, id));
            used[id] = true;
        }
        writer.println(ans);
        writer.close();
    }

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