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 Solution
{
    static int N,M;
    static long dp[][];
    static int mod=(int)1e9+7;
    public static void main(String ag[])
    {
        Scanner sc=new Scanner(System.in);
        int i,j,k;
        N=sc.nextInt();
        M=2*sc.nextInt();
        dp=new long[M+1][N+1];
        
        for(i=0;i<=M;i++)
        for(j=0;j<=N;j++)
        dp[i][j]=-1;
        System.out.println(find(0,1));
    }
    
    public static long find(int pos,int lastValue)
    {
        if(pos==M||lastValue==N)
        return 1;
        
        if(dp[pos][lastValue]!=-1)
        return dp[pos][lastValue];
        
        long total=0;
        total=(total+find(pos,lastValue+1)%mod)%mod;
        total%=mod;
        total=(total+find(pos+1,lastValue)%mod)%mod;
        total%=mod;
        
        return dp[pos][lastValue]=total;
    }
}