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.math.*;

public class Main {

    public static BigInteger fact(BigInteger x) {
        // if (x.compareTo(BigInteger.ONE) == 0) {
        //     return BigInteger.ONE;
        // } else {
        //     return x.multiply(fact(x.subtract(BigInteger.ONE)));
        // }
        BigInteger cnt=BigInteger.ONE;
        BigInteger lat=BigInteger.ONE;
        while (cnt.compareTo(x)<=0){
            lat = lat.multiply(cnt);
            cnt=cnt.add(BigInteger.ONE);
        }
        return lat;
    }

    public static void main(String[] args) {
        Scanner cin = new Scanner(System.in);
        BigInteger n = cin.nextBigInteger();
        BigInteger m = cin.nextBigInteger();
        BigInteger mod = BigInteger.valueOf(1000000007);
        BigInteger fenzi = fact(n.add(m.multiply(BigInteger.valueOf(2)).subtract(BigInteger.ONE)));
        BigInteger fenmu = fact(m.multiply(BigInteger.valueOf(2))).multiply(fact(n.subtract(BigInteger.ONE)));
        fenzi = fenzi.divide(fenmu);
        fenzi = fenzi.mod(mod);
        System.out.println(fenzi);
    }

}