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.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner sc=new Scanner (System.in);
		int mod= (int) (1e9+7);
		int n=sc.nextInt();
		int m=sc.nextInt();
		int f[][]=new int [1005][1005];
		for(int i=1;i<=n;i++) 
			f[1][i]=  1; 
		for(int i=2;i<=2*m;i++)
			for(int j=1;j<=n;j++){
	            f[i][j]=f[i][j-1]+f[i-1][j];
	            f[i][j]%=mod;
	        }
		
		Long ans=(long) 0;
		for(int i=1;i<=n;i++)
		{
			ans=(ans+f[2*m][i])%mod;//�ڸó���Ϊ2m���������һ��λ�÷�1~n�����֮��
		}
	
		System.out.println(ans);
	}

}
