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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class TEST {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] tokens = br.readLine().split(" ");
		int N = Integer.parseInt(tokens[0]);
		int M = Integer.parseInt(tokens[1]);
		int[][] dp = new int[N + 1][M * 2 + 1];
		// dp[Max Val][Max Len]
		for (int i = 1; i < M * 2 + 1; i++) {
			dp[1][i] = 1;
		}
		for (int i = 1; i <= N; i++) {
			dp[i][1] = i;
		}
		for (int i = 2; i <= N; i++) {
			for (int j = 2; j <= M * 2; j++) {
				dp[i][j] = (dp[i - 1][j] + dp[i][j - 1]) % (int) (1e9 + 7);
			}
		}
		System.out.println(dp[N][M * 2]);
	}
}
