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.*;
public class TwoArrays{
	public static void main(String[]args){
		Scanner in = new Scanner(System.in);  
		int n,m;
		int mod=(int)1e9+7;
		n=in.nextInt();
		m=in.nextInt();
		long[][]dp=new long[2*m+1][n+1];
		Arrays.fill(dp[1],1);
		dp[1][0]=0;
		for(int i=2;i<=n;i++)dp[1][i]+=dp[1][i-1];
		for(int i=2;i<=2*m;i++){
			dp[i][0]=0;
			for(int j=1;j<=n;j++){dp[i][j]=dp[i-1][j]+dp[i][j-1];dp[i][j]%=mod;
				//System.out.println("i= "+i+" j= "+j+" "+dp[i][j]);
			}
		}
		//long ans=0;
		//for(long x:dp[2*m]){ans+=x;ans%=mod;}
		System.out.println(dp[2*m][n]);
	}
}