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]. 
//I got sick, so decided to do coding, then there is this power cut. God this is not good :(
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.*;
public class Main
{

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static void main(String[] args)
    {
        FastReader sc=new FastReader();

        StringBuilder sb=new StringBuilder();
        int n=sc.nextInt();
        int m=sc.nextInt()+1;
long mod=1000000007;
        long dp[][]=new long[n][m];

        for( int i=0;i<m;i++)
        {
          if(i==0)
          {
            for( int d=0;d<n;d++)
            {
              dp[d][i]=1;

            }
            continue;
          }
          for( int j=1;j<=n;j++)
          {
            for( int k=j;k<=n;k++)
            {
              dp[k-1][i]=(dp[k-1][i]%mod+(dp[j-1][i-1]%mod*(k-j+1)%mod)%mod)%mod;
              dp[k-1][i]%=mod;
            }
          }
        }
        System.out.println(dp[n-1][m-1]%mod);


    }

}

class Pair implements Comparable<Pair>
{
  long first;int  sec;
  Pair( long first, int sec)
  {
    this.first=first;
    this.sec=sec;
  }
  @Override
  public int compareTo( Pair a)
  {
    return Long.compare( a.first, this.first);
  }
}
