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.Arrays;
import java.util.Scanner;

public class D_277 {
	MyScanner sc = new MyScanner();
	final int MOD = 1000000007;

	int d, n;
	int[] a, f;
	ArrayList<Integer>[] g;
	boolean[] v;

	@SuppressWarnings("unchecked")
	void run() {
		d = sc.nextInt();
		n = sc.nextInt();
		a = sc.nextIntArray(n);
		f = new int[n];
		v = new boolean[n];
		g = new ArrayList[n];
		for (int i = 0; i < n; i++)
			g[i] = new ArrayList<Integer>();
		for (int i = 0; i < n - 1; i++) {
			int s = sc.nextInt() - 1;
			int t = sc.nextInt() - 1;
			g[s].add(t);
			g[t].add(s);
		}

		int result = 0;
		for (int i = 0; i < n; i++) {
			Arrays.fill(v, false);
			Arrays.fill(f, 0);
			dfs(i, i);
			result = (result + f[i]) % MOD;
		}
		System.out.println(result);
	}

	void dfs(int u, int root) {
		v[u] = true;
		f[u] = 1;
		for (int next : g[u]) {
			if (!v[next]) {
				if (a[next] < a[root] || a[next] > a[root] + d) continue;
				if (a[next] == a[root] && next < root)          continue;
				dfs(next, root);
				f[u] = (int)(((long)f[u] * (f[next] + 1)) % MOD);
			}
		}
	}

	public static void main(String[] args) {
		new D_277().run();
	}

	void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	void debug2(char[][] array) {
		for (int i = 0; i < array.length; i++) {
			for (int j = 0; j < array[i].length; j++) {
				System.out.print(array[i][j]);
			}
			System.out.println();
		}
	}

	boolean inner(int h, int w, int limH, int limW) {
		return 0 <= h && h < limH && 0 <= w && w < limW;
	}

	void swap(int[] x, int a, int b) {
		int tmp = x[a];
		x[a] = x[b];
		x[b] = tmp;
	}

	// find minimum i (a[i] >= border)
	int lower_bound(int a[], int border) {
		int l = -1;
		int r = a.length;
		while (r - l > 1) {
			int mid = (l + r) / 2;
			if (border <= a[mid]) {
				r = mid;
			} else {
				l = mid;
			}
		}
		// r = l + 1
		return r;
	}

	boolean palindrome(String s) {
		for (int i = 0; i < s.length() / 2; i++) {
			if (s.charAt(i) != s.charAt(s.length() - 1 - i)) {
				return false;
			}
		}
		return true;
	}

	class MyScanner {
		int nextInt() {
			try {
				int c = System.in.read();
				while (c != '-' && (c < '0' || '9' < c))
					c = System.in.read();
				if (c == '-')
					return -nextInt();
				int res = 0;
				do {
					res *= 10;
					res += c - '0';
					c = System.in.read();
				} while ('0' <= c && c <= '9');
				return res;
			} catch (Exception e) {
				return -1;
			}
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		String next() {
			try {
				StringBuilder res = new StringBuilder("");
				int c = System.in.read();
				while (Character.isWhitespace(c))
					c = System.in.read();
				do {
					res.append((char) c);
				} while (!Character.isWhitespace(c = System.in.read()));
				return res.toString();
			} catch (Exception e) {
				return null;
			}
		}

		int[] nextIntArray(int n) {
			int[] in = new int[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextInt();
			}
			return in;
		}

		int[][] nextInt2dArray(int n, int m) {
			int[][] in = new int[n][m];
			for (int i = 0; i < n; i++) {
				in[i] = nextIntArray(m);
			}
			return in;
		}

		double[] nextDoubleArray(int n) {
			double[] in = new double[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextDouble();
			}
			return in;
		}

		long[] nextLongArray(int n) {
			long[] in = new long[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextLong();
			}
			return in;
		}

		char[][] nextCharField(int n, int m) {
			char[][] in = new char[n][m];
			for (int i = 0; i < n; i++) {
				String s = sc.next();
				for (int j = 0; j < m; j++) {
					in[i][j] = s.charAt(j);
				}
			}
			return in;
		}
	}
}