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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

import javax.jws.soap.SOAPBinding.Use;


public class D {

    static StringTokenizer st;
    static BufferedReader br;
    static PrintWriter pw;
    static int d;
    static ArrayList<Integer>[]ages;
    static long[]dp;
    static boolean[][]f;
    static class Sort implements Comparable<Sort> {
        int val, ind;
        public int compareTo(Sort arg0) {
            return this.val-arg0.val;
        }
    }
    static boolean[]used;
    static int mod = (int) (1e9+7);
    static int min, from;
    static int[]a;
    static long ans;
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        d = nextInt();
        int n = nextInt();
        Sort[]b = new Sort[n+1];
        ages = new ArrayList[n+1];
        a = new int[n+1];
        f = new boolean[n+1][n+1];
        for (int i = 1; i <= n; i++) {
            b[i] = new Sort();
            b[i].val = nextInt();
            b[i].ind = i;
            a[i] = b[i].val;
            ages[i] = new ArrayList<>();
        }
        Arrays.sort(b, 1, n+1);
        for (int i = 1; i < n; i++) {
            int v = nextInt();
            int u = nextInt();
            ages[v].add(u);
            ages[u].add(v);
        }
        used = new boolean[2001];
        dp = new long[n+1];
        for (int i = 1; i <= n; i++) {
            min = b[i].val;
            Arrays.fill(dp, 1);
            from = b[i].ind;
            dfs(b[i].ind, 0);
            ans = (ans+dp[b[i].ind]) % mod;
        }
        for (int i = 1; i <= n; i++) {
            if (used[i]) {
                ans = (ans+1) % mod;
            }
        }
        System.out.println(ans);
        pw.close();
    }
    private static void dfs(int v, int p) {
        f[from][v] = true;
        for (int to : ages[v]) {
            if (to==p || a[to] < min || a[to] > min+d)
                continue;
            if (a[to]==min && f[to][from]) {
                continue;
            }
            dfs(to, v);
            dp[v] = dp[v] * (dp[to]+1) % mod;
        }
    }
    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    private static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    private static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    private static String next() throws IOException {
        while (st==null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
}
