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.lang.*;
import java.io.*;
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
	    Scanner sc=new Scanner(System.in);
	   // BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	    int t=1;
	   // t=sc.nextInt();
	    long M=1000000007l;
	    //int t=Integer.parseInt(br.readLine());
	    while(--t>=0){
	        int n=sc.nextInt();
	        int m=sc.nextInt();
	        long dp[][]=new long[m+1][n+1];
	        for(int i=1;i<=n;i++)
	        	dp[1][i]=1l;
	        
	        for(int i=2;i<=m;i++) {
	        	long temp=0;
	        	for(int j=1;j<=n;j++) {
	        		temp=(temp+dp[i-1][j])%M;
	        		dp[i][j]=temp;
	        	}
	        }
	    
	        long ans=0;
	        long dp1[]=new long[n+1];
	        for(int i=1;i<=n;i++) {
	        	dp1[i]=(dp1[i-1]+dp[m][i])%M;
	        }
	        
	        for(int i=1;i<=n;i++) {
	        	ans=(ans+(dp[m][i]*dp1[n-i+1])%M)%M;
	        	//System.out.println(ans);
	        }
	        System.out.println(ans);
	    }
	    
	}
}