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.
//package codeforce;
import java.io.*;
import java.util.*;
public class ValidSets {
    static ArrayList<ArrayList<Integer>> x;
    static int[] a;
    static int d;
    static long mod=(long)(1e9+7L);
public static void main(String[] args) throws Exception
{
    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    String[] temp=br.readLine().split(" ");
     d=Integer.parseInt(temp[0]);
    int n=Integer.parseInt(temp[1]);
    a=new int[n];
    x=new ArrayList<ArrayList<Integer>>();
    temp=br.readLine().split(" ");
    for(int i=0;i<n;i++)
    {
        a[i]=Integer.parseInt(temp[i]);
        x.add(new ArrayList<Integer>());
    }
    for(int i=0;i<n-1;i++)
    {
        temp=br.readLine().split(" ");
        int u=Integer.parseInt(temp[0])-1;
        int v=Integer.parseInt(temp[1])-1;
        x.get(u).add(v);
        x.get(v).add(u);
        
    }
    long ans=0;
    for(int h=0;h<n;h++)
    {
        long th=dfs(h,-1,h);
        ans=(ans+th)%mod;
        
    }
    System.out.println(ans);
    
}
static long dfs(int curr,int prev,int fornode)
{
    ArrayList<Integer> temp=x.get(curr);
    long ret=1;
    if(a[curr]<a[fornode])
        return 0;
    if(a[curr]>a[fornode]+d)
        return 0;
    if(a[curr]==a[fornode] && curr>fornode)
    {
        return 0;
    }
    int count=0;
    for(int j=0;j<temp.size();j++)
    {

        int y=temp.get(j);
        if(y==prev)
            continue;
        else
        {
            long ans=dfs(y,curr,fornode);
            
            
            ret*=(ans+1);
            ret=ret%mod;
            
        }
    }
    

        return ret;
    

    
    
}

}
