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.*;
public class c {
        static Scanner in=new Scanner(System.in);
        static long[][] ncr;
        public static void main(String[] args) {
                ncr=numCombinations(3000,1000000007);
                int n=in.nextInt(),m=in.nextInt();
                System.out.println(sab(2*m+1,n-1));
        }
        private static long sab(int size, int count) {//stars and bars
                return ncr[count+size-1][count];
        }
        public static long[][]  numCombinations(int max, int mod){
                long[][] ans=new long[max][max];
                for(int i=0;i<max;i++)ans[i][0]=1;
                for(int i=1;i<max;i++)for(int j=1;j<max;j++)ans[i][j]=(ans[i-1][j]+ans[i-1][j-1])%mod;
                return ans;
        }
}