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.*;
import java.io.*;
public class afterALongTime1 {
    public static int mod=(int)(1e9+7);
	public static void main(String[] args) throws Exception{
	Scanner scn=new Scanner(System.in);
    int n=scn.nextInt();
    int m=scn.nextInt();
    long[]arr=new long[(2*m)+1];
    arr[0]=1L;
    for(int i=0;i<=(n+(2*m)-1);i++){
        long[]temp=new long[(2*m)+1];
        temp[0]=1L;
        for(int j=1;j<=i && j<=(2*m);j++){
            temp[j]=(arr[j]+arr[j-1])%mod;
        }
        arr=temp;
    }
    System.out.println(arr[2*m]);
    }
}