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 validsets;
import java.util.*;
import java.io.*;
public class Validsets
{
	static class Reader
	{
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader()
		{
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException
		{
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException
		{
			byte[] buf = new byte[201]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1)
			{
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException
		{
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do
			{
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException
		{
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			}
			while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException
		{
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			}
			while ((c = read()) >= '0' && c <= '9');

			if (c == '.')
			{
				while ((c = read()) >= '0' && c <= '9')
				{
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException
		{
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException
		{
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException
		{
			if (din == null)
				return;
			din.close();
		}
	}
        static int a[],pa[];static LinkedList<Integer> ll[];static long mod=(long)1E9+7;
        static long dfs(int n,int r,long d){
         ListIterator it=ll[n].listIterator();
         long ans=1;
         while(it.hasNext()){
          int c=(int)it.next();
          if(pa[c]==0){
           pa[c]=n;
           if((a[r]>a[c]&&a[r]-a[c]<=d)||(a[r]==a[c]&&r<c)){
            ans=(ans*(dfs(c,r,d)+1))%mod;
           }
          }
         }return ans;
        }
        public static void main(String[] args) throws IOException
	{
		Reader in=new Reader();PrintWriter out=new PrintWriter(System.out);
                int d=in.nextInt(),n=in.nextInt();
                a=new int[n+1];pa=new int[n+1];ll=new LinkedList[n+1];
                for(int i=1;i<=n;i++)a[i]=in.nextInt();
                for(int i=0;i<=n;i++)ll[i]=new LinkedList<>();
                for(int i=0;i<n-1;i++){int u=in.nextInt(),v=in.nextInt();ll[u].add(v);ll[v].add(u);}
                long ans=0;
                for(int i=1;i<n+1;i++){
                 for(int j=0;j<n+1;j++)pa[j]=0;pa[i]=i;
                 ans=(ans+dfs(i,i,d))%mod;//out.println(ans);
                }out.print(ans);
                out.flush();out.close();
	}
}