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.BufferedReader;
import java.io.File;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import static java.lang.Math.*;
import static java.util.Arrays.*;

public class Main {

	public static void main(String[] args) throws IOException {
		new Main().run();
	}

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");

	private void run() throws IOException {
		if (new File("input.txt").exists())
			in = new BufferedReader(new FileReader("input.txt"));
		else
			in = new BufferedReader(new InputStreamReader(System.in));
		if (new File("output.txt").exists())
			out = new PrintWriter("output.txt");
		else
			out = new PrintWriter(System.out);

		solve();

		in.close();
		out.close();
	}

	final int maxn = 2000 + 100;
	final int maxm = 2 * maxn;
	final long mod = 1000 * 1000 * 1000 + 7;

	int n, d;
	int a[] = new int[maxn];

	int cnt;
	int head[] = new int[maxn];
	int next[] = new int[maxm];
	int to[] = new int[maxm];

	boolean used[] = new boolean[maxn];

	void add(int u, int v, boolean needInverse) {
		to[cnt] = v;
		next[cnt] = head[u];
		head[u] = cnt++;

		if (needInverse)
			add(v, u, false);
	}

	long dfs(int v, int p, int maxVal) {
		long ans = 1;
		for (int i = head[v]; i > -1; i = next[i])
			if (to[i] != p)
				if ((a[to[i]] < maxVal && maxVal - a[to[i]] <= d) || (a[to[i]] == maxVal && !used[to[i]])) {
					long t = dfs(to[i], v, maxVal) + 1;
					ans = (ans * t) % mod;
				}
		return ans;
	}

	void solve() throws IOException {
		fill(head, -1);
		d = nextInt();
		n = nextInt();
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		for (int i = 0; i < n - 1; i++) {
			int u = nextInt() - 1;
			int v = nextInt() - 1;
			add(u, v, true);
		}

		long ans = 0;
		for (int v = 0; v < n; v++) {
			used[v] = true;
			long t = dfs(v, -1, a[v]);
			ans = (ans + t) % mod;
		}

		out.println(ans);
	}

	String nextLine() throws IOException {
		st = new StringTokenizer("");
		return in.readLine();
	}

	String nextToken() throws IOException {
		while (!st.hasMoreTokens()) {
			st = new StringTokenizer(in.readLine());
		}
		return st.nextToken();
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

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

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

	boolean EOF() throws IOException {
		while (!st.hasMoreTokens()) {
			String str = in.readLine();
			if (str == null)
				return true;
			st = new StringTokenizer(str);
		}
		return false;
	}

}
