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.io.*;

public class CostOfDancing {
 	
	public static long getCount(List<Integer>[] edge,int[] value,int r,int c,int d,int[] close){
		long v=1;
		close[c]=1;
		for(int ei : edge[c]){
			if(close[ei]!=0)
				continue;
			if(value[r]<value[ei]||(value[r]==value[ei]&&ei>r)||(value[ei]<value[r]-d))
				continue;
			v=((1+getCount(edge,value,r,ei,d,close))*v)%1000000007;
		}
		return v;
	}
	
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int d, n;
		d = s.nextInt();
		n = s.nextInt();

		List<Integer>[] edge = new List[n];
		int[] v = new int[n];
		for (int i = 0; i < n; i++){
			edge[i] = new Vector<>();
			v[i]=s.nextInt();
		}
		
		for(int i=0;i<n-1;i++){
			int a,b;
			a=s.nextInt();
			b=s.nextInt();
			
			edge[a-1].add(b-1);
			edge[b-1].add(a-1);
		}
		
		long sum=0;
		for(int i=0;i<n;i++){
			sum=(sum+getCount(edge,v,i,i,d,new int[n]))%1000000007;
		}
		System.out.println(sum);
	}

}
