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 Div2;

import java.util.ArrayList;
import java.util.Scanner;

public class CF277 {
	private static final int MAXN = 2010;
	private static final long MOD = (int)1e9 + 7;

	private static ArrayList<Integer>[] adj = new ArrayList[MAXN];
	private static int[] a = new int[MAXN];
	private static long[] f = new long[MAXN];
	private static boolean[] visited = new boolean[MAXN];

	private static int d, n;
	
	private static void DFS(int u, int root){
		visited[u] = true;
		f[u] = 1;
		for(int i=0; i<adj[u].size(); i++){
			int v = adj[u].get(i);
			if(!visited[v]){
				if((a[v] < a[root]) || (a[v] > a[root] +d)) continue;
				if((a[v] == a[root]) && (v < root)) continue;
				DFS(v, root);
				f[u] = f[u] * (f[v] + 1) % MOD;
			}
		}
	}
	
	public static void main(String[] args){
		Scanner input = new Scanner(System.in);
		d = input.nextInt();
		n = input.nextInt();
				
		for(int i=1; i<=n; i++){
			adj[i] = new ArrayList<Integer>();
			a[i] = input.nextInt();
		}
		for(int i=1; i<=n-1; i++){
			int u, v;
			u = input.nextInt();
			v = input.nextInt();
			adj[u].add(v);
			adj[v].add(u);
		}
		input.close();
		
		long result = 0;
		for(int i=1; i<=n; i++){
			for(int j=1; j<=n; j++){
				f[j] = 0;
				visited[j] = false;
			}
			DFS(i, i);
			result = (result + f[i]) % MOD;
		}
		
		System.out.println(result);
	}
}
