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 A {
    static int mod = 1000000007;
    static int fact[];

    static int size;

    static long ncr(int n, int r) {

        if (r > n)
            return 0;
        return fact[n] * power(fact[r], mod - 2) % mod * power(fact[n - r], mod - 2) % mod;
    }

    static long power(long a, long b) {
        long res = 1;
        while (b != 0) {
            if (b % 2 == 1)
                res = res * a % mod;
            b >>= 1;
            a = a * a % mod;
        }
        return res;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        StringBuilder sb = new StringBuilder();

        int n = sc.nextInt();
        int m = sc.nextInt();

        int size = 1050;

        fact = new int[size];
        fact[0] = 1;
        fact[1] = 1;
        for (int i = 2; i < size; i++) {
            fact[i] = (int) ((i * (long) fact[i - 1]) % mod);
        }

        sb.append(ncr(2 * m + n - 1, 2 * m)).append("\n");

        System.out.print(sb);
    }
}