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]. 
// package Jan28;

import java.lang.reflect.Array;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;

public class C {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m  = sc.nextInt();
        double[][] grid = new double[n][2*m]; //row then col
        for (int i=0;i<n;i++) {
            Array.set(grid[i], 0, 1);
        }


        for (int j=1;j<(2*m);j++) {
            double sofar = 0;
            for (int i=n-1; i>-1;i--) {
                sofar += grid[i][j-1];
                sofar = (sofar % (Math.pow(10, 9) + 7));
                Array.set(grid[i], j, (grid[i][j] + sofar) % (Math.pow(10, 9) + 7));
            }
        }

//ARR printer
//        for (int i=0; i<n;i++) {
//            for (int j=0;j<(2*m);j++) {
//                System.out.println(grid[i][j]);
//            }
//        }


        double res = 0;

        for (int a=0;a<n;a++) {
            res += grid[a][2*m - 1];
            res = res % (Math.pow(10, 9) + 7);
        }

        System.out.println((int) res);
    }


}
