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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;


public class R277qDValidSets {

	static int n,d;
	static ArrayList<Integer> g[];
	static int a[];
	static long mod = (long)(1e9 + 7);
	
	@SuppressWarnings("unchecked")
	public static void main(String args[] ) throws Exception {
		   
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    PrintWriter w = new PrintWriter(System.out);
	    
	    StringTokenizer st1 = new StringTokenizer(br.readLine());
	    d = ip(st1.nextToken());
		n = ip(st1.nextToken());
	          
	    StringTokenizer st2 = new StringTokenizer(br.readLine());
	    a = new int[n];
	    for(int i=0;i<n;i++)
	    	a[i] = ip(st2.nextToken());
	        
	    g = new ArrayList[n];
		for(int i=0;i<n;i++)
			g[i] = new ArrayList<Integer>();
		for(int i=1;i<n;i++){
			StringTokenizer st = new StringTokenizer(br.readLine());
			int u = ip(st.nextToken()) - 1;
			int v = ip(st.nextToken()) - 1;
			g[u].add(v);
			g[v].add(u);
		}
		
		long ans = 0;
		for(int i=0;i<n;i++){
			ans += dfs(i,-1,i) + mod - 1;
			if(ans >= mod)	ans %= mod;
		}
		
		w.println(ans);
	    w.close(); 
	}
	
	public static long dfs(int curr,int prev,int minID){
		if(a[curr] < a[minID])	return 1;
		if(a[curr] == a[minID] && curr < minID)	return 1;
		if(a[curr] > a[minID] + d)	return 1;
		
		long ret = 1;
		int s = g[curr].size();
		for(int i=0;i<s;i++){
			if(g[curr].get(i) == prev)	continue;
			ret *= dfs(g[curr].get(i),curr,minID);
			if(ret >= mod)	ret %= mod;
		}
		
		return ret + 1;
	}
	
	public static int ip(String s){
		return Integer.parseInt(s);
	}
	
}
