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.InputStreamReader;
import java.math.BigInteger;
import java.util.*;
import java.util.stream.LongStream;
public class TwoArray {
	public static long factt( long n )
	{
	    return LongStream.rangeClosed( 1, n )
	                     .reduce(1, ( long a, long b ) -> a * b);
	}
	public static BigInteger fact(int num) {
	    BigInteger result = BigInteger.ONE;
	    for (int i = 1; i <= num; i++)
	        result = result.multiply(BigInteger.valueOf(i));
	    return result;
	}
	
	public static void main (String[] args) throws java.lang.Exception
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    String s[]=br.readLine().split(" ");
	    int n=Integer.parseInt(s[0]);
	    int m=Integer.parseInt(s[1]);
	    int k=2*m;
	    n=(n + 2*m - 1);
	    BigInteger n_k=fact(n-k);
	    System.out.println((fact(n).divide((fact(k).multiply(n_k)))).mod(BigInteger.valueOf(1000000007)));
	}

}
