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.*;

// 11111119
// 99999999
//dp[i][a][b]+= (a<=(i-1a))
public class CF {
	private static void sport(int n, int m) {
		long[][] dp = new long[2 * m][n + 1];
		int mod = (int) (1e9 + 7);
		for (int i = 1; i < n + 1; i++) {
			dp[0][i] = 1;
		}
		for (int i = 1; i < 2 * m; i++) {
			for (int j = 1; j < n + 1; j++) {
				for (int k = j; k >= 0; k--) {
					dp[i][j] += dp[i - 1][k];
					dp[i][j] %= mod;
				}
			}
		}
		long ans = 0;
		for (long l : dp[2*m - 1]) {
			ans += l;
			ans %= mod;
		}
		System.out.println(ans);
	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		sport(n, m);
	}
}