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 _32_Valid_Sets {

	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		int d = scn.nextInt();
		int n = scn.nextInt();
		int[] arr = new int[n];
		ArrayList<ArrayList<Integer>> adjac = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			arr[i] = scn.nextInt();
			adjac.add(new ArrayList<>());
		}
		for (int i = 0; i < n - 1; i++) {
			int val = scn.nextInt() - 1;
			int val2 = scn.nextInt() - 1;
			adjac.get(val).add(val2);
			adjac.get(val2).add(val);
		}
		long ans = 0;
		for (int i = 0; i < n; i++) {
			ArrayList<ArrayList<Integer>> nt = new ArrayList<>();
			for (int j = 0; j < n; j++) {
				nt.add(new ArrayList<>());
			}
			dfs(i, -1, adjac, nt, i, arr, d);
			long[] dp = new long[n];
			long val = calculate(i, -1, nt, dp);
			ans = (ans + val) % mod;
		}
		System.out.println(ans);
	}

	static long mod = 1000000007;

	private static long calculate(int i, int j, ArrayList<ArrayList<Integer>> nt, long[] dp) {
		for (int val : nt.get(i)) {
			if(val==j){
				continue;
			}
			calculate(val, i, nt, dp);
		}
		long val = 1;
		for (int l : nt.get(i)) {
			
			if(l==j){
				continue;
			}
				
			val = (val * (dp[l] + 1)) % mod;
		}
		dp[i] = val;
		return val;
	}

	public static void dfs(int vertex, int parent, ArrayList<ArrayList<Integer>> graph,
			ArrayList<ArrayList<Integer>> mygraph, int strt, int[] arr, int d) {
		if (parent != -1) {
			mygraph.get(vertex).add(parent);
			mygraph.get(parent).add(vertex);
		}
		for (int i : graph.get(vertex)) {
			if (i == parent) {
				continue;
			}
			if (arr[i] > arr[strt] && arr[i] <= arr[strt] + d) {
				dfs(i, vertex, graph, mygraph, strt, arr, d);
			}else if(arr[i]==arr[strt]&&i<strt){
				dfs(i, vertex, graph, mygraph, strt, arr, d);
			}
		}
	}

}
