





'''simple docstring'''






from itertools import product






def      __A						(							a_						:  int      ,a_						:  int	):
		lowerCAmelCase     :    Optional[Any]						=   sides_number
		lowerCAmelCase     :    Optional[int]						=   max_face_number * dice_number
		lowerCAmelCase     :    List[Any]						=   [0] * (max_total + 1)

		lowerCAmelCase     :    Optional[int]						=   1
		lowerCAmelCase     :    str						=   range(a_      ,max_face_number + 1	)
		for dice_numbers in product(a_      ,repeat=a_	):
				lowerCAmelCase     :    Union[str, Any]						=   sum(a_	)
				totals_frequencies[total] += 1

		return totals_frequencies






def      __A						(							):
		lowerCAmelCase     :    Union[str, Any]						=   total_frequency_distribution(
		    sides_number=4      ,dice_number=9	)
		lowerCAmelCase     :    Union[str, Any]						=   total_frequency_distribution(
		    sides_number=6      ,dice_number=6	)

		lowerCAmelCase     :    Any						=   0
		lowerCAmelCase     :    Any						=   9
		lowerCAmelCase     :    int						=   4 * 9
		lowerCAmelCase     :    List[Any]						=   6
		for peter_total in range(a_      ,max_peter_total + 1	):
				peter_wins_count += peter_totals_frequencies[peter_total] * sum(
				    colin_totals_frequencies[min_colin_total:peter_total]	)

		lowerCAmelCase     :    List[str]						=   (4**9) * (6**6)
		lowerCAmelCase     :    Optional[Any]						=   peter_wins_count / total_games_number

		lowerCAmelCase     :    Optional[int]						=   round(a_      ,ndigits=7	)

		return rounded_peter_win_probability


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










'''simple docstring'''






from ...utils import (
    OptionalDependencyNotAvailable,
    is_torch_available,
    is_transformers_available,
    is_transformers_version,
)


try:
					if not (is_transformers_available() and is_torch_available()):
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from ...utils.dummy_torch_and_transformers_objects import KandinskyPipeline, KandinskyPriorPipeline
else:
					from .pipeline_kandinsky import KandinskyPipeline
					from .pipeline_kandinsky_imgaimg import KandinskyImgaImgPipeline
					from .pipeline_kandinsky_inpaint import KandinskyInpaintPipeline
					from .pipeline_kandinsky_prior import KandinskyPriorPipeline, KandinskyPriorPipelineOutput
					from .text_encoder import MultilingualCLIP



