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.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;

public class R277D2D {
    static final int MOD = (int)1e9+7;
    static int[] cursor, edges, a;
    static boolean[] visited, checked;
    static int d;
    static int count(int i, int max){
        long ret = 1;
        visited[i] = true;
        for(int e=cursor[i]; e<cursor[i+1]; e++){
            int j = edges[e];
            if(!checked[j] && !visited[j] && max>=a[j] && max-a[j]<=d){
                ret = (ret*(count(j, max)+1))%MOD;
            }
        }
        return (int)ret;
    }
    static class Node implements Comparable<Node>{
        int index; int value;
        public Node(int index, int value){
            this.index = index;
            this.value = value;
        }

        @Override
        public int compareTo(Node o) {
            return o.value-this.value;
        }
    }
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        d = Integer.parseInt(st.nextToken());
        int n = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(br.readLine());
        a = new int[n];
        for(int i=0; i<n; i++){
            a[i] = Integer.parseInt(st.nextToken());
        }

        cursor = new int[n+1];

        int[] x = new int[n-1];
        int[] y = new int[n-1];
        for(int i=0; i<n-1; i++){
            st = new StringTokenizer(br.readLine());
            x[i] = Integer.parseInt(st.nextToken())-1;
            y[i] = Integer.parseInt(st.nextToken())-1;
            cursor[x[i]]++;
            cursor[y[i]]++;
        }
        for(int i=0; i<n; i++) cursor[i+1] += cursor[i];

        edges = new int[2*(n-1)];
        for(int i=0; i<n-1; i++){
            edges[--cursor[x[i]]] = y[i];
            edges[--cursor[y[i]]] = x[i];
        }

        Node[] nodes = new Node[n];
        for(int i=0; i<n; i++){
            nodes[i] = new Node(i, a[i]);
        }
        Arrays.sort(nodes);

        visited = new boolean[n];
        checked = new boolean[n];
        int ret = 0;
        for(int i=0; i<n; i++){
            Arrays.fill(visited, false);
            ret = (ret + count(nodes[i].index, nodes[i].value))%MOD;
            checked[nodes[i].index] = true;
        }

        System.out.println(ret);

    }
}
