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.Scanner;

public class C {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt();
        int p = 1000000007;
        long[][] c = new long[1101][1101];
        c[0][0] = 1;
        for (int i=1; i<=1100; i++) {
            c[i][0] = 1; c[i][i] = 1;
            for (int j=1; j<i; j++) {
                c[i][j] = (c[i-1][j] + c[i-1][j-1]) % p;
            }
        }
        long sum = 0;
        for (int A=1; A<=n; A++) {
            sum += c[A+m-2][m-1] * c[n-A+m][m];
            sum = sum % p;
        }
        System.out.println(sum);
    }
}
