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]. 
// No sorceries shall prevail. //           
import java.util.*;
import java.io.*;
	
public class InVoker {	
	
	static long mod = 1000000007;
	public static void main(String args[]) {
			
		Scanner inp=new Scanner(System.in);
		PrintWriter out=new PrintWriter(System.out);
		
		int n=inp.nextInt();
		int m=inp.nextInt();
		long ways[][]=new long[n][2*m+1];
		for(int i=0;i<n;i++) {
			ways[i][0]=1;
		}
		for(int j=0;j<=2*m;j++) {
			ways[0][j]=1;
		}
		for(int i=1;i<n;i++) {
			for(int j=1;j<=2*m;j++) {
				ways[i][j]=(ways[i-1][j]%mod + ways[i][j-1]%mod)%mod;
			}
		}
		out.println(ways[n-1][2*m]);
		out.close();
		inp.close();
	}
}
