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 Solution{
	static PrintWriter out=new PrintWriter(System.out);
	public static void main (String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
		String[] temp=br.readLine().trim().split(" ");
		
		int n=Integer.parseInt(temp[0]);
		int m=Integer.parseInt(temp[1]);
		out.println(numWays(n,m));
		
		out.flush();
		out.close();
	}
	public static int numWays(int n,int m){
	    int[][][] dp=new int[m][n+1][n+1];
	    for(int i=0;i<m;i++){
	        for(int j=0;j<n+1;j++){
	            for(int k=0;k<n+1;k++){
	                dp[i][j][k]=-1;
	            }
	        }
	    }
	    return numWaysHelper(0,1,n,m,dp);
	}
	public static int numWaysHelper(int index,int lower,int upper,int m,int[][][] dp)
	{
	    if(index==m){
	        return 1;
	    }
	    if(lower>upper)
	    {
	        return 0;
	    }
	    if(dp[index][lower][upper]>=0){
	        return dp[index][lower][upper];
	    }
	    int mod=1000000000+7;
	    int ans1=numWaysHelper(index,lower+1,upper,m,dp);
	    int ans2=numWaysHelper(index,lower,upper-1,m,dp);
	    int ans3=numWaysHelper(index,lower+1,upper-1,m,dp);
	    int ans4=numWaysHelper(index+1,lower,upper,m,dp);
	    int ans=((((ans1%mod)+(ans2%mod))%mod)+(ans4%mod))%mod;
	    ans=((ans%mod)-(ans3%mod)+mod)%mod;
	    dp[index][lower][upper]=ans;
	    return ans;
	}
}