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.Arrays;
import java.util.Scanner;

public class que3 {

	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		
			int n = scn.nextInt();
			int m = scn.nextInt();
			long[][] arr = new long[n + 1][m + 1];
			Arrays.fill(arr[1], 1);
			for (int i = 1; i <= n; i++) {
				arr[i][1] = 1;
			}
			long mod = 1000000007;
			for (int i = 2; i <= n; i++) {
				for (int j = 2; j <= m; j++) {
					for (int v = 1; v <= i; v++) {
						arr[i][j] = (arr[i][j] + arr[v][j - 1]) % mod;
					}
				}
			}
			long ans = 0;
			for (int i = 1; i <= n; i++) {
				long val = arr[i][m];
				long val2 = 0;
				for (int j = i; j <= n; j++) {
					val2 = (val2 + arr[n + 1 - j][m]) % mod;
				}
				ans = ((val * val2) % mod + ans) % mod;
			}
			System.out.println(ans);
		}
		
	}


