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.*;
public class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(System.out);
        String str[]=br.readLine().split(" ");
        int n=Integer.parseInt(str[0]);
        int m=Integer.parseInt(str[1]);
        long arr[][]=new long[m+1][n+1];
        long sum[][]=new long[m+1][n+1];
        long mod=1000000007;
        for(int i=1;i<=n;i++)
        {
            arr[1][i]=((long)i*(i+1)/2)%mod;
            sum[1][i]+=(sum[1][i-1]%mod+arr[1][i]%mod)%mod;
        }
        for(int i=2;i<=m;i++)
        {
            for(int j=1;j<=n;j++)
            {
                arr[i][j]=(sum[i-1][j]%mod+arr[i][j-1]%mod)%mod;
                sum[i][j]=(sum[i][j]%mod+sum[i][j-1]%mod+arr[i][j]%mod)%mod;
            }
        }
        pw.println(arr[m][n]);
        pw.flush();
        pw.close();
    }
}