

def 							_lowerCamelCase   (			SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE   ):
      '''simple docstring'''







      if number < 0 or shift_amount < 0:
            raise ValueError('''both inputs must be positive integers'''   )

      A_							       =		str(bin(SCREAMING_SNAKE_CASE   )   )
      binary_number += "0" * shift_amount
      return binary_number







def 							_lowerCamelCase   (			SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE   ):
      '''simple docstring'''







      if number < 0 or shift_amount < 0:
            raise ValueError('''both inputs must be positive integers'''   )

      A_							       =		str(bin(SCREAMING_SNAKE_CASE   )   )[2:]
      if shift_amount >= len(SCREAMING_SNAKE_CASE   ):
            return "0b0"
      A_							       =		binary_number[: len(SCREAMING_SNAKE_CASE   ) - shift_amount]
      return "0b" + shifted_binary_number







def 							_lowerCamelCase   (			SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE   ):
      '''simple docstring'''







      if number >= 0:  # Get binary representation of positive number
            A_							       =		'''0''' + str(bin(SCREAMING_SNAKE_CASE   )   ).strip('''-'''   )[2:]
      else:  # Get binary (2's complement) representation of negative number
            A_							       =		len(bin(SCREAMING_SNAKE_CASE   )[3:]   )  # Find 2's complement of number
            A_							       =		bin(abs(SCREAMING_SNAKE_CASE   ) - (1 << binary_number_length)   )[3:]
            A_							       =		(
                '''1''' + '''0''' * (binary_number_length - len(SCREAMING_SNAKE_CASE   )) + binary_number
            )

      if shift_amount >= len(SCREAMING_SNAKE_CASE   ):
            return "0b" + binary_number[0] * len(SCREAMING_SNAKE_CASE   )
      return (
          "0b"
          + binary_number[0] * shift_amount
          + binary_number[: len(SCREAMING_SNAKE_CASE   ) - shift_amount]
      )


if __name__ == "__main__":
      import doctest

      doctest.testmod()








from itertools import product







def 							_lowerCamelCase   (			SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE   ):
      '''simple docstring'''







      A_							       =		sides_number
      A_							       =		max_face_number * dice_number
      A_							       =		[0] * (max_total + 1)

      A_							       =		1
      A_							       =		range(SCREAMING_SNAKE_CASE		,				max_face_number + 1   )
      for dice_numbers in product(SCREAMING_SNAKE_CASE		,				repeat=SCREAMING_SNAKE_CASE   ):
            A_							       =		sum(SCREAMING_SNAKE_CASE   )
            totals_frequencies[total] += 1

      return totals_frequencies







def 							_lowerCamelCase   (			):
      '''simple docstring'''







      A_							       =		total_frequency_distribution(
          sides_number=4		,				dice_number=9   )
      A_							       =		total_frequency_distribution(
          sides_number=6		,				dice_number=6   )

      A_							       =		0
      A_							       =		9
      A_							       =		4 * 9
      A_							       =		6
      for peter_total in range(SCREAMING_SNAKE_CASE		,				max_peter_total + 1   ):
            peter_wins_count += peter_totals_frequencies[peter_total] * sum(
                colin_totals_frequencies[min_colin_total:peter_total]   )

      A_							       =		(4**9) * (6**6)
      A_							       =		peter_wins_count / total_games_number

      A_							       =		round(SCREAMING_SNAKE_CASE		,				ndigits=7   )

      return rounded_peter_win_probability


if __name__ == "__main__":
      print(f'{solution() = }')





