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.ArrayList;
import java.util.Scanner;

public class Main {
	
	private static final int MAX_RESULT = 1000000007;
	private static int maxDiff = 0;
	
	private static class Node{
		public int index;
		public int value;
		public ArrayList<Node> neighbors;
		
		public Node(int index, int value){
			this.index = index;
			this.value = value;
			this.neighbors = new ArrayList<Node>();
		}
	}
	
	private static long nValidSubsets(Node root, Node currNode, Node currParent){
		if (currNode.value < root.value){
			return 0;
		} else if (currNode.value == root.value && currNode.index < root.index){
			// to avoid double counting; stop traversing tree if node has:
			// 1. same value as root, 2. smaller index than root
			return 0;
		} else if (currNode.value - root.value > maxDiff){
			return 0;
		} else {
			long nValidSubsets = 1;
			ArrayList<Node> neighbors = currNode.neighbors;
			for (Node neighbor: neighbors){
				if (neighbor != currParent){
					long temp = nValidSubsets * (nValidSubsets(root, neighbor, currNode) + 1);
					nValidSubsets = temp % MAX_RESULT;
				}
			}
			return nValidSubsets;
		}
	}
	
	public static void main(String[] args){
		Scanner in = new Scanner(System.in);
		maxDiff = in.nextInt();
		int nNodes = in.nextInt();
		
		// get all the nodes
		Node[] allNodes = new Node[nNodes];
		for (int i = 0; i < nNodes; i++){
			allNodes[i] = new Node(i, in.nextInt());
		}
		
		// add all connections
		for (int i = 0; i < nNodes - 1; i++){
			Node node1 = allNodes[in.nextInt() - 1];
			Node node2 = allNodes[in.nextInt() - 1];
			node1.neighbors.add(node2);
			node2.neighbors.add(node1);
		}
		
		long result = 0;
		for (Node node: allNodes){
			result = ((result + nValidSubsets(node, node, null)) % MAX_RESULT);
		}
		
		System.out.println(result);
		in.close();
	}
	
}
