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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class UnshuffeledDeck {
    public static void main(String[] args) {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int n=input.nextInt();
        int m=input.nextInt();
        BigInteger a=new BigInteger(String.valueOf(n+2*m-1));
        a=fac(a);
        BigInteger b=new BigInteger(String.valueOf(2*m));
        b=fac(b);
        BigInteger c=new BigInteger(String.valueOf(n-1));
        c=fac(c);
        BigInteger ans=new BigInteger("1");
        ans=ans.multiply(a);
        ans=ans.divide(b);
        ans=ans.divide(c);
        ans=ans.mod(new BigInteger("1000000007"));
        out.println(ans.toString());
        out.close();
    }
    public static BigInteger fac(BigInteger b)
    {
        if(b.toString().equals("0"))
        {
            return new BigInteger("1");
        }
        else
        {
            BigInteger b1=b;
            b1=b1.subtract(new BigInteger("1"));
            return b.multiply(fac(b1));
        }
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}
