


"""simple docstring"""
from __future__ import annotations

import math
import random






def 						lowercase				(	_snake_case		: int	,  _snake_case		: int	,  _snake_case		: int	)	->list[int]:
	"""simple docstring"""





	__snake_case      :		Tuple         =							d * e - 1
	__snake_case      :		List[str]         =							0
	__snake_case      :		Dict         =							0
	while p == 0:
		__snake_case      :		str         =							random.randint(2	,  n - 1	)
		__snake_case      :		int         =							k
		while True:
			if t % 2 == 0:
				__snake_case      :		int         =							t // 2
				__snake_case      :		int         =							(g**t) % n
				__snake_case      :		Optional[Any]         =							math.gcd(x - 1	,  _snake_case	)
				if x > 1 and y > 1:
					__snake_case      :		Tuple         =							y
					__snake_case      :		int         =							n // y
					break  # find the correct factors
			else:
				break  # t is not divisible by 2, break and choose another g
	return sorted([p, q]	)


if __name__ == "__main__":
			import doctest

			doctest.testmod()









'''simple docstring'''


import torch
from torch import autograd






class 						lowerCAmelCase__      (      autograd.Function						):




			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  Optional[int]						,	lowerCamelCase__	:  torch.tensor						,	lowerCamelCase__	:  float						,	lowerCamelCase__	:  bool			) ->Optional[Any]:



					'''simple docstring'''







					_UpperCAmelCase		:							Optional[int]             =   inputs.numel()
					_UpperCAmelCase		:							Any             =   int(0.0_0_5 * nb_elems			) + 1
					if sigmoid:
							_UpperCAmelCase		:							List[str]             =   (torch.sigmoid(lowerCamelCase__			) > threshold).type(inputs.type()			)
					else:
							_UpperCAmelCase		:							List[Any]             =   (inputs > threshold).type(inputs.type()			)
					if mask.sum() < nb_min:
							# We limit the pruning so that at least 0.5% (half a percent) of the weights are remaining
							_UpperCAmelCase		:							str             =   inputs.flatten().kthvalue(max(nb_elems - nb_min						,	1			)			).values
							_UpperCAmelCase		:							str             =   (inputs > k_threshold).type(inputs.type()			)
					return mask






			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  List[Any]						,	lowerCamelCase__	:  Optional[int]			) ->Dict:



					'''simple docstring'''







					return gradOutput, None, None






class 						lowerCAmelCase__      (      autograd.Function						):




			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  Optional[int]						,	lowerCamelCase__	:  torch.tensor						,	lowerCamelCase__	:  float			) ->List[str]:



					'''simple docstring'''







					_UpperCAmelCase		:							Optional[int]             =   inputs.clone()
					_UpperCAmelCase       ,     _UpperCAmelCase		:							Tuple             =   inputs.flatten().sort(descending=lowerCamelCase__			)
					_UpperCAmelCase		:							Optional[int]             =   int(threshold * inputs.numel()			)

					# flat_out and mask access the same memory.
					_UpperCAmelCase		:							str             =   mask.flatten()
					_UpperCAmelCase		:							Optional[int]             =   0
					_UpperCAmelCase		:							Optional[Any]             =   1
					return mask






			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  Optional[int]						,	lowerCamelCase__	:  Any			) ->Union[str, Any]:



					'''simple docstring'''







					return gradOutput, None






class 						lowerCAmelCase__      (      UpperCAmelCase__						):




			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  torch.tensor						,	lowerCamelCase__	:  float			) ->Tuple:



					'''simple docstring'''







					_UpperCAmelCase		:							List[Any]             =   inputs.clone()
					_UpperCAmelCase       ,     _UpperCAmelCase		:							Optional[Any]             =   inputs.abs().flatten().sort(descending=lowerCamelCase__			)
					_UpperCAmelCase		:							int             =   int(threshold * inputs.numel()			)

					# flat_out and mask access the same memory.
					_UpperCAmelCase		:							int             =   mask.flatten()
					_UpperCAmelCase		:							List[Any]             =   0
					_UpperCAmelCase		:							int             =   1
					return mask



