def binomial(n, k):
    if k == 0 or k == n:
        return 1
    return binomial(n - 1, k) + binomial(n - 1, k - 1)

def binomial_A(n, k):
    result = 1
    for i in range(k):
        result = result * (n - i) // (k - i)
    return result

def binomial_B(n, k):
    result = 1
    for i in range(k)[::-1]:
        result = result * (n - i) // (k - i)
    return result