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.*;
import java.util.*;

public class Codeforces
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();
        String s[]=bu.readLine().split(" ");
        int d=Integer.parseInt(s[0]),n=Integer.parseInt(s[1]),i;
        ArrayList<Integer> g[]=new ArrayList[n];
        for(i=0;i<n;i++)
        g[i]=new ArrayList<>();

        int a[]=new int[n];
        s=bu.readLine().split(" ");
        for(i=0;i<n;i++)
        a[i]=Integer.parseInt(s[i]);
        for(i=0;i<n-1;i++)
        {
            s=bu.readLine().split(" ");
            int u=Integer.parseInt(s[0]),v=Integer.parseInt(s[1]);
            u--; v--;
            g[u].add(v);
            g[v].add(u);
        }

        long dp[]=new long[n],M=1000000007,ans=0;

        for(i=0;i<n;i++)
        {
            dfs(g,dp,a,i,-1,i,d);
            ans+=dp[i];
            ans%=M;

        }
        System.out.print(ans);
    }

    static void dfs(ArrayList<Integer> g[],long dp[],int a[],int n,int p,int c,int d)
    {
        long M=1000000007;
        dp[n]=1;
        for(int x:g[n])
        if(x==p) continue;
        else if((a[c]>a[x] || (a[x]==a[c] && c>=x)) && a[c]-a[x]<=d)
        {
            dfs(g,dp,a,x,n,c,d);
            dp[n]+=dp[n]*dp[x]%M;
            dp[n]%=M;
        }
    }
}