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 Main {
	static Graph G;
	static int[] a;
	static int d;
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		d = scanner.nextInt();
		int n = scanner.nextInt();
		a = new int[n];
		for(int i = 0; i < n; i++) {
			a[i] = scanner.nextInt();
		}
		G = new Graph(n);
		for(int i = 0; i < n-1; i++) {
			G.addEdge(scanner.nextInt() - 1, scanner.nextInt() - 1);
		}
		long sum = 0;
		for(int i = 0; i < n; i++) {
			sum += dfs(i, -1, a[i], i);
			sum %= 1000000007;
		}
		System.out.println(sum);
	}
	private static long dfs(int v, int pre, int min, int root) {
		if(a[v] < min || a[v] > min + d || a[v] == min && v < root) return 0;
		long val = 1;
		for(int neighbor : G.getNeighbors(v)) {
			if(neighbor != pre) {
				val *= (dfs(neighbor, v, min, root)+1);
				val %= 1000000007;
			}
		}
		return val;
	}
	
	
}
class Graph {
	private int n;
	private List<List<Integer>> adj;
	
	public Graph(int n) {
		this.n = n;
		adj = new ArrayList<List<Integer>>();
		for(int i = 0; i < n; i++) {
			adj.add(new LinkedList<Integer>());
		}
	}
	
	public int getSize() {
		return n;
	}
	
	public void addEdge(int e1, int e2) {
		adj.get(e1).add(e2);
		adj.get(e2).add(e1);
	}
	
	public List<Integer> getNeighbors(int v) {
		return adj.get(v);
	}
	

}
