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]. 
def solve():
    MOD = 10**9 + 7
    nm = input().split()
    n = int(nm[0])
    m = int(nm[1])
    C = [[1 for _ in range(n+m)] for _ in range(m+1)]
    for i in range(m+1):
        for j in range(i, n+m):
           # print(i, j)
            if (i == j):
                C[i][j] = 1
            elif (i == 0):
                C[i][j] = 1
            else:
                C[i][j] = (C[i][j-1] + C[i-1][j-1]) % MOD

    result = 0
    for i in range(1, n+1):
        #print(f'C{m}{i+m-1}, C{m}{n-i+m}')
        numA = C[m][i+m-1]
        numA = numA % MOD

        numB = C[m-1][n-i+m-1]
        numB = numB % MOD

        result += (numA * numB) % MOD
        result = result % MOD
    print(result)


solve()
