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.*;
import java.util.*;
public final class valid_sets
{
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	static FastScanner sc=new FastScanner(br);
    static PrintWriter out=new PrintWriter(System.out);
	static Random rnd=new Random();
	static long mod=(long)(1e9+7);
	static int maxn=(int)(2e3)+3;
	static ArrayList<Integer>[] al;
	static int[] a;
	static long[][] dp;
	
	static int check(int curr,int low)
	{
		return (curr==low?1:0);
	}
	
	static void dfs(int u,int p,int low,int high)
	{
		for(int x:al[u])
		{
			if(x!=p)
			{
				dfs(x,u,low,high);
			}
		}
		if(a[u]>=low && a[u]<=high)
		{
			dp[check(a[u],low)][u]=1;long tot=1;
			for(int x:al[u])
			{
				if(x!=p)
				{
					long now=(dp[0][x]+dp[1][x])%mod;
					tot=(tot*(now+1))%mod;
				}
			}
			tot=(tot-1+mod)%mod;long curr=1;
			for(int x:al[u])
			{
				if(x!=p)
				{
					curr=(curr*(dp[0][x]+1))%mod;
				}
			}
			curr=(curr-1+mod)%mod;
			if(a[u]==low)
			{
				dp[1][u]=(dp[1][u]+tot)%mod;
			}
			else
			{
				dp[0][u]=(dp[0][u]+curr)%mod;dp[1][u]=(tot-curr+mod)%mod;
			}
		}
	}
	
	@SuppressWarnings("unchecked")
    public static void main(String args[]) throws Exception
    {
		int d=sc.nextInt(),n=sc.nextInt();al=new ArrayList[maxn];a=new int[n];long res=0;
		for(int i=0;i<n;i++)
		{
			a[i]=sc.nextInt();al[i]=new ArrayList<Integer>();
		}
		for(int i=1;i<n;i++)
		{
			int u=sc.nextInt()-1,v=sc.nextInt()-1;
			al[u].add(v);al[v].add(u);
		}
		for(int i=1;i<=2000;i++)
		{
			dp=new long[2][n];dfs(0,-1,i,i+d);long curr=0;
			for(int j=0;j<n;j++)
			{
				curr=(curr+dp[1][j])%mod;
			}
			res=(res+curr)%mod;
		}
		out.println(res);out.close();
    }
}
class FastScanner
{
    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in) {
        this.in = in;
    }
	
    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
	
	public String next() throws Exception {
		return nextToken().toString();
	}
	
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}