

'''simple docstring'''

class 							_snake_case :
   def __init__( self			:      Optional[int]     ,SCREAMING_SNAKE_CASE__			:      list[int]							):
     SCREAMING_SNAKE_CASE:Tuple						      =					len(SCREAMING_SNAKE_CASE__							)
     SCREAMING_SNAKE_CASE:List[str]						      =					[0] * len_array

     if len_array > 0:
       SCREAMING_SNAKE_CASE:List[Any]						      =					array[0]

     for i in range(1     ,SCREAMING_SNAKE_CASE__							):
       SCREAMING_SNAKE_CASE:int						      =					self.prefix_sum[i - 1] + array[i]
   def     __UpperCamelCase						( self			:      Tuple     ,SCREAMING_SNAKE_CASE__			:      int     ,SCREAMING_SNAKE_CASE__			:      int							):
     if start == 0:
       return self.prefix_sum[end]

     return self.prefix_sum[end] - self.prefix_sum[start - 1]







   def     __UpperCamelCase						( self			:      Optional[int]     ,SCREAMING_SNAKE_CASE__			:      int							):
     SCREAMING_SNAKE_CASE:Optional[int]						      =					{0}
     for sum_item in self.prefix_sum:
       if sum_item - target_sum in sums:
         return True

       sums.add(SCREAMING_SNAKE_CASE__							)

     return False


if __name__ == "__main__":
    import doctest

    doctest.testmod()









'''simple docstring'''

from math import factorial





def    A_  ( snake_case      ,       snake_case ):

  # If either of the conditions are true, the function is being asked
  # to calculate a factorial of a negative number, which is not possible
  if n < k or k < 0:
    raise ValueError("Please enter positive integers for n and k where n >= k" )
  return factorial(snake_case ) // (factorial(snake_case ) * 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.",
    )






