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.*;

public class Solution {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt(); int b = sc.nextInt();

        BigInteger combination = compute_combination(a+2*b-1,2*b);

        System.out.println(combination.mod(BigInteger.valueOf(1000000007)));
    }

    private static BigInteger compute_combination(int n, int r) {
        int min = Math.min(n-r,r); int max = n-min;
        BigInteger prod = BigInteger.ONE; BigInteger div = BigInteger.ONE;
        for(int i=n;i>max;i--){
            prod = prod.multiply( BigInteger.valueOf(i));
        }
        for(int i=min;i>1;i--){
            div = div.multiply( BigInteger.valueOf(i));
        }
        return prod.divide(div);
    }
}
