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.io.File;
import java.io.FileNotFoundException;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Scanner;
import java.util.StringTokenizer;

public class l086 {
	
	private static long mod = (long)1e9+7;
	
	private static long tot = 0;
	
	private static int[] a = null;
	
	private static int d = 0;

	public static void main(String[] args) throws Exception {
//		StringTokenizer stok = new StringTokenizer(new Scanner(new File("F:/books/input.txt")).useDelimiter("\\A").next());
		StringTokenizer stok = new StringTokenizer(new Scanner(System.in).useDelimiter("\\A").next());
		StringBuilder sb = new StringBuilder();
		d = Integer.parseInt(stok.nextToken());
		int n = Integer.parseInt(stok.nextToken());
		a = new int[n+1];
		for(int i=1;i<=n;i++) a[i] = Integer.parseInt(stok.nextToken()); 
		ArrayList<Integer>[] G = new ArrayList[n + 1];
		for (int i = 0; i <= n; i++)
			G[i] = new ArrayList<Integer>();
		for (int i = 0; i < n-1; i++) {
			int u = Integer.parseInt(stok.nextToken());
			int v = Integer.parseInt(stok.nextToken());
			G[u].add(v);
			G[v].add(u);
		}
		for(int i=1;i<=n;i++) dfsTree(G,i);
		System.out.println(tot);
	}
	
	private static void dfsTree(ArrayList<Integer>[] G, int s) {
		int n = G.length;
		boolean[] visited= new boolean[n];
		int[] ss = new int[n];
		ArrayDeque<Integer> S = new ArrayDeque<Integer>();
		long[] dp = new long[G.length];
		S.add(s);
		int min = a[s];
		while(!S.isEmpty()) {
			int c = S.pop();
			if(visited[c]!=true) {
				visited[c] = true;
				if(a[c]<min || (a[c]==min && c<s) || a[c]>min+d) continue;
				while(ss[c]<G[c].size() && visited[G[c].get(ss[c])]) ss[c]++;
				if(ss[c]==G[c].size()) {
					dp[c] = 1;
				}
				else {
					S.push(c);
					S.push(G[c].get(ss[c]));
				}
			}
			else {
				//
				ss[c]++;
				while(ss[c]<G[c].size() && visited[G[c].get(ss[c])]) ss[c]++;
				if(ss[c]==G[c].size()) {
					dp[c]=1;
					for(int v : G[c]) {
						dp[c] = (dp[c]*(1+dp[v]))%mod;
					}
				}
				else {
					S.push(c);
					S.push(G[c].get(ss[c]));
				}
			}
		}
		tot = (tot + dp[s])%mod;
	}

}
