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.util.*;
 
public class ValidSets {
	static final long MOD = 1000000007;
	static ArrayList<LinkedList<Integer>> tree = new ArrayList<LinkedList<Integer>>();
	static int[] a;
	static int d, n;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		d = sc.nextInt();
		n = sc.nextInt();
		a = new int[n];
		for(int i = 0; i < n; i++) {
			tree.add(new LinkedList<Integer>());
			a[i] = sc.nextInt();
		}
		for(int i = 0; i < n - 1; i++) {
			int u = sc.nextInt() - 1, v = sc.nextInt() - 1;
			tree.get(u).add(v);
			tree.get(v).add(u);
		}
		sc.close();
		long ans = 0;
		for(int i = 0; i < n; i++)
			ans = (ans + f(i, -1, a[i], i) - 1) % MOD;
		System.out.println(ans);
	}
	static long f(int i, int p, int max, int x) {
		long res = 1;
		for(int j : tree.get(i))
			if(j != p && ((a[j] == max && j < x) || (a[j] < max && a[j] >= max - d)))
				res = res * f(j, i, max, x) % MOD;
		return res + 1;
	}
}