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 ECR80C {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextInt();
        long m = sc.nextInt();

        System.out.println(C(n + 2 * m - 1, 2 * m).mod(BigInteger.valueOf((long) (1e9 + 7))));
    }

    public static BigInteger C(long n, long k) {
        BigInteger a = BigInteger.ONE, b = BigInteger.ONE;
        k = Math.max(k, n - k);
        for (long i = k + 1; i <= n; i++) {
            a = a.multiply(BigInteger.valueOf(i));
            b = b.multiply(BigInteger.valueOf(i - k));
        }
        return a.divide(b);
    }
}
