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.*;

public class Main {
    static long d(int x, int y, int mod) {
        long result = 0;

        long[] prev = new long[y + 1];
        long[] current = new long[y + 1];
        Arrays.fill(current, 1);  // level x == 0
        
        for (int i = 0; i < x; i++) {
            // in current level x == i
            prev = current;
            for (int j = 2; j < prev.length; j++) {
                current[j] = (prev[j] + current[j - 1]) % mod;
            }
        }


        return current[y];
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int m = sc.nextInt();

        System.out.println(d(2*m, n, 1_000_000_000 + 7));
    } 
}