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 CF;
import java.util.*;
public class cf277_2d {
	static ArrayList<ArrayList<Integer>> adj = new ArrayList<ArrayList<Integer>>();
	static long[] f;
	static long[] w;
	static boolean[] visited;
	static int d,n;
	static long mod = 1000000007;
	
	static void dfs(int u,int root) {
		visited[u] = true;
		f[u]=1;
		int size = adj.get(u).size();
		ArrayList<Integer> lis = adj.get(u);
		for (int i = 0; i < size; i++) {
			int v = lis.get(i);
			if(!visited[v]) {
				if(w[v]<w[root]||w[v]>w[root]+d) continue;
				if(w[v]==w[root]&&v<root) continue;
				dfs(v,root);
				f[u] = ((f[u]%mod)*((f[v]+1)%mod))%mod;
			}
		}
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		d = sc.nextInt();
		n = sc.nextInt();
		w = new long[n];
		f = new long [n];
		visited = new boolean[n];
		for (int i = 0; i < n; i++) {
			w[i]=sc.nextLong();
		}
		
		for (int i = 0; i < n; i++) {
			adj.add(new ArrayList<Integer>());
		}
		
		for (int i = 0; i < n-1; i++) {
			int a = sc.nextInt()-1;
			int b = sc.nextInt()-1;
			adj.get(a).add(b);
			adj.get(b).add(a);
		}
		
		long ret = 0;
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				visited[j] = false;
				f[j] = 0;
			}
			dfs(i,i);
			
			ret = ((ret%mod)+(f[i]%mod))%mod;
		}
		
		System.out.println(ret);
		
		sc.close();
	}

}
