You are given two integers n and m. Calculate the number of pairs of arrays (a, b) such that:

  * the length of both arrays is equal to m; 
  * each element of each array is an integer between 1 and n (inclusive); 
  * a_i ≤ b_i for any index i from 1 to m; 
  * array a is sorted in non-descending order; 
  * array b is sorted in non-ascending order. 



As the result can be very large, you should print it modulo 10^9+7.

Input

The only line contains two integers n and m (1 ≤ n ≤ 1000, 1 ≤ m ≤ 10).

Output

Print one integer – the number of arrays a and b satisfying the conditions described above modulo 10^9+7.

Examples

Input


2 2


Output


5


Input


10 1


Output


55


Input


723 9


Output


157557417

Note

In the first test there are 5 suitable arrays: 

  * a = [1, 1], b = [2, 2]; 
  * a = [1, 2], b = [2, 2]; 
  * a = [2, 2], b = [2, 2]; 
  * a = [1, 1], b = [2, 1]; 
  * a = [1, 1], b = [1, 1]. 
import java.util.*;
import java.io.*;
import java.math.BigInteger;
import static java.lang.Math.*;
 
public class Main
{
	static final int mod = (int)1e9+7;
	public static void main(String[] args) throws Exception
	{
		FastReader in = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int test = 1;
		while(test-- > 0)
		{
			int n = in.nextInt();
			int m = in.nextInt();
			long[] dp = new long[n + 1];
			Arrays.fill(dp, 1);
			for(int i = 1; i < m + m; i++) {
				long prefix = 0;
				for(int j = 1; j <= n; j++) {
					prefix = (prefix + dp[j]) % mod;
					dp[j] = prefix;
				}
			}
			long ans = 0;
			for(int i = 1; i <= n; i++) {
				ans = (ans + dp[i]) % mod;
			}
			out.println(ans);
		}
		out.flush();
	}
}
 
class FastReader
{
	BufferedReader br;
	StringTokenizer st;
 
	public FastReader()
	{
	    br = new BufferedReader(new InputStreamReader(System.in));
	}
 
	public String next() throws IOException
	{
	    if(st == null || !st.hasMoreElements())
	    {
	        st = new StringTokenizer(br.readLine());
	    }

	    return st.nextToken();
	}
 
	public int nextInt() throws IOException
	{
	    return Integer.parseInt(next());
	}
 
	public long nextLong() throws IOException
	{
	    return Long.parseLong(next());
	}
 
	public String nextLine() throws IOException
	{
		return br.readLine();
	}
}