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.*;
import java.lang.*;
import java.lang.Math.*;
import java.io.*;

public class cf_276_A {

	public static boolean[] f = new boolean[2020];
	public static long MOD  = 1000000007;
	public static  int n,d;
	public static int[] a = new int[2020];
	public static int[][] b = new int[2020][2020];
	public static long res  = 0;
	public static int[] c = new int[2020];
	public static int delta;
	
	public static long dfs(int p, int v)
	{
		if (c[v]>delta + d || ((c[v] == delta + d) && (f[v] == true)) || c[v]<delta)
			  return 0;
		long ans = 1;
		for (int i = 1; i <=a[v]; i++)
		{
			int u = b[v][i];
			if (u!=p)
			  ans = ans*( (dfs(v,u) + 1)% MOD);
			  ans = ans % MOD;
		}
		return ans;
	}
	
	public static void main(String[] args) throws java.lang.Exception
	{
	  Scanner reader = new Scanner(System.in);
	  d = reader.nextInt();
	  n = reader.nextInt();
	  int u,v;
	  for (int i=1; i<=n; i++) c[i] = reader.nextInt();
	  for (int i=1; i<n; i++)
	  {
		  u = reader.nextInt();
		  v = reader.nextInt();
		  a[u]++;
		  a[v]++;
		  b[u][a[u]] = v;
		  b[v][a[v]] = u;
	  }
	  
	  for (int i=1; i<=n; i++)
	  {
		  delta = c[i] - d;
		  res = (res + dfs(i,i)) % MOD;
		  f[i] = true;
	  }
	 System.out.print(res);
	}
}
