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.math.*;
import java.io.*;
import java.text.*;
public class Main
{
    public static BigInteger Factorial(BigInteger n,BigInteger m)
    {
        BigInteger ans=BigInteger.ONE;
        for(BigInteger i=BigInteger.ONE;i.compareTo(m)<=0;i=i.add(BigInteger.ONE))
            ans=ans.multiply(n.subtract(m).add(i)).divide(i);
        return ans;
    }
    public static final BigInteger mod=BigInteger.valueOf(1000000007);
    public static void main(String args[])throws IOException
    {
        StreamTokenizer st=new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        PrintWriter pw=new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
        BigInteger n,m;
        st.nextToken();
        n=BigInteger.valueOf((int)st.nval);
        st.nextToken();
        m=BigInteger.valueOf((int)st.nval);
        pw.println(Factorial(n.add(BigInteger.valueOf(2).multiply(m).subtract(BigInteger.ONE)),BigInteger.valueOf(2).multiply(m)).mod(mod));
        pw.close();
    }
}