

'''simple docstring'''





from math import factorial


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		int ,   _SCREAMING_SNAKE_CASE					:		int       ):





    """simple docstring"""


    if n < k or k < 0:
        raise ValueError('Please enter positive integers for n and k where n >= k'       )
    return factorial(A__       ) // (factorial(A__       ) * factorial(n - k       ))


if __name__ == "__main__":
       print(
           "The number of five-card hands possible from a standard",
           F'fifty-two card deck is: {combinations(52, 5)}\n',
       )

       print(
           "If a class of 40 students must be arranged into groups of",
           F'4 for group projects, there are {combinations(40, 4)} ways',
           "to arrange them.\n",
       )

       print(
           "If 10 teams are competing in a Formula One race, there",
           F'are {combinations(10, 3)} ways that first, second and',
           "third place can be awarded.",
       )





def 					_UpperCAmelCase       (  ):





    """simple docstring"""


    for n in range(1 ,   1_000_000       ):
        yield n * (n + 1) // 2


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		Tuple       ):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_									=						1
    SCREAMING_SNAKE_CASE_									=						2
    while i * i <= n:
        SCREAMING_SNAKE_CASE_									=						0
        while n % i == 0:
            n //= i
            multiplicity += 1
        divisors_count *= multiplicity + 1
        i += 1
    if n > 1:
        divisors_count *= 2
    return divisors_count


def 					_UpperCAmelCase       (  ):





    """simple docstring"""


    return next(i for i in triangle_number_generator() if count_divisors(_SCREAMING_SNAKE_CASE       ) > 500       )


if __name__ == "__main__":
       print(solution())


