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 valid_set {
	static int mod = (int) (1e9 + 7);
	static int d;
	static ArrayList<Integer>[] g;
	static boolean visited[];

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scn = new Scanner(System.in);
		d = scn.nextInt();

		int n = scn.nextInt();
		g = new ArrayList[n];
		long dp[] = new long[n];
		int val[] = new int[n];
		for (int i = 0; i < n; i++) {
			val[i] = scn.nextInt();
			g[i] = new ArrayList<>();
		}
		for (int i = 0; i < n - 1; i++) {
			int x = scn.nextInt() - 1;
			int y = scn.nextInt() - 1;
			g[x].add(y);
			g[y].add(x);
		}
		long ans = 0;
		for (int i = 0; i < n; i++) {
			dp = new long[n];
			visited = new boolean[n];
			dfs(dp, i,i, val);
			ans = (ans + dp[i]) % mod;
		}
		System.out.println(ans);

	}

	private static void dfs(long[] dp, int i, int root,int[] val) {
		dp[i] = 1;
		visited[i] = true;
		for (int nei : g[i]) {
			if (visited[nei])
				continue;
			if (val[nei] < val[root] || val[nei] > val[root] + d)
				continue;
			if (val[nei] == val[root] && nei < root)
				continue;
			dfs(dp, nei, root,val);
			dp[i] = (dp[i] * (dp[nei] + 1)) % mod;
		}
		
	}

}

