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.math.BigInteger;
import java.util.Scanner;

public class C1288 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int M = in.nextInt();
        int mod = 1000000007;
        BigInteger up = BigInteger.ONE;
        BigInteger down = BigInteger.ONE;
        for (int x=1; x<=2*M; x++) {
            up = up.multiply(BigInteger.valueOf(2*M+N-x));
            down = down.multiply(BigInteger.valueOf(x));
        }
        int result = up.divide(down).mod(BigInteger.valueOf(mod)).intValue();
        System.out.println(result);
    }

}
