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.*;
import java.util.*;

public class Bricks {
	
	 static int nCrModpDP(int n, int r, int p) 
	 { 
	     
	     int[] C=new int[r+1]; 
	   
	     C[0] = 1; 
	   
	     for (int i = 1; i <= n; i++) 
	     { 
	         for (int j = Math.min(i, r); j > 0; j--) 
	   
	             C[j] = (C[j] + C[j-1])%p; 
	     } 
	     return C[r]; 
	 } 
	   
	 
	 static int nCrModpLucas(int n, int r, int p) 
	 { 
	
	 if (r==0) 
	     return 1; 
	 
	 int ni = n%p; 
	 int ri = r%p; 
	
	 return (nCrModpLucas(n/p, r/p, p) *  
	         nCrModpDP(ni, ri, p)) % p; 
	 }
	
	public static void main(String []argh){
        Scanner s=new Scanner(System.in);
      
         long n=s.nextLong();
       long m=s.nextLong();
       long p=1000000007;
       System.out.println(nCrModpLucas((int)(n+2*m-1),(int)(2*m),(int)p));
        
    }
}
