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.*;
import java.util.*;

public class Code {

	public static long ncr(int n, int r) {
		long[][] dp = new long[n+1][r+1];
		for (int i=0; i<=n; i++) {
			for (int j=0; j<=Math.min(i, r); j++) {
				if (j == 0 || j == i) {
					dp[i][j] = 1;
				}else {
					dp[i][j] = (dp[i-1][j] + dp[i-1][j-1])%1000000007;
				}
			}
		}
		return dp[n][r];
	}
	

	public static void main(String[] args) throws IOException
	{
		// BufferedReader br = new BufferedReader(new FileReader("input.txt"));
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] lines = br.readLine().trim().split(" ");
		int n = Integer.parseInt(lines[0]);
		int m = Integer.parseInt(lines[1]);
		System.out.println(ncr(n-1+(2*m), 2*m));
	}
}
