




def  UpperCAmelCase_							(				__UpperCAmelCase						:     int							) ->			list[int]:

      if length <= 0 or not isinstance(__UpperCAmelCase      ,      __UpperCAmelCase							):
            raise ValueError('Length must be a positive integer.'							)
      return [n * (2 * n - 1) for n in range(__UpperCAmelCase							)]


if __name__ == "__main__":
   print(hexagonal_numbers(length=5))
   print(hexagonal_numbers(length=10))





def  UpperCAmelCase_							(				__UpperCAmelCase						:     Optional[Any]      ,      __UpperCAmelCase						:     Union[str, Any]							) ->			List[str]:
      SCREAMING_SNAKE_CASE_     						=      0
      while b > 0:
            if b & 1:
                  res += a

            a += a
            b >>= 1

      return res

def  UpperCAmelCase_							(				__UpperCAmelCase						:     str      ,      __UpperCAmelCase						:     int      ,      __UpperCAmelCase						:     Tuple							) ->			int:
      SCREAMING_SNAKE_CASE_     						=      0
      while b > 0:
            if b & 1:
                  SCREAMING_SNAKE_CASE_     						=      ((res % c) + (a % c)) % c

            a += a
            b >>= 1

      return res