'''simple docstring'''
from __future__ import annotations

import math
import random







def 			_UpperCamelCase			(  _a						:						List[Any]					,  _a						:						Optional[Any]					,  _a						:						Union[str, Any]      ):




    """simple docstring"""



    __UpperCamelCase						:						int		     =	d * e - 1
    __UpperCamelCase						:						List[str]		     =	0
    __UpperCamelCase						:						int		     =	0
    while p == 0:
        __UpperCamelCase						:						int		     =	random.randint(2					,  n - 1      )
        __UpperCamelCase						:						List[str]		     =	k
        while True:
            if t % 2 == 0:
                __UpperCamelCase						:						Optional[int]		     =	t // 2
                __UpperCamelCase						:						int		     =	(g**t) % n
                __UpperCamelCase						:						Any		     =	math.gcd(x - 1					,  lowercase_      )
                if x > 1 and y > 1:
                    __UpperCamelCase						:						List[str]		     =	y
                    __UpperCamelCase						:						Optional[Any]		     =	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"""


from typing import List, Optional, Tuple, Union

import torch

from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput







class  A_     (	SCREAMING_SNAKE_CASE_							):



						"""simple docstring"""






						def __init__(   self					:List[str]  ,    lowercase_					:List[str]  ,    lowercase_					:List[Any]   )							->     List[str]:
												super().__init__()
												self.register_modules(unet=lowercase_  ,    scheduler=lowercase_   )






						@torch.no_grad()
						def __call__(   self					:int  ,    lowercase_					:int = 1  ,    lowercase_					:Optional[Union[torch.Generator, List[torch.Generator]]] = None  ,    lowercase_					:int = 10_00  ,    lowercase_					:Optional[str] = "pil"  ,    lowercase_					:bool = True  ,    )							->     Union[ImagePipelineOutput, Tuple]:
												# Sample gaussian noise to begin loop
												if isinstance(self.unet.config.sample_size  ,    lowercase_   ):
																		UpperCAmelCase			 =					(
																		    batch_size,
																		    self.unet.config.in_channels,
																		    self.unet.config.sample_size,
																		    self.unet.config.sample_size,
																		)
												else:
																		UpperCAmelCase			 =					(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

												if self.device.type == "mps":
																		# randn does not work reproducibly on mps
																		UpperCAmelCase			 =					randn_tensor(lowercase_  ,    generator=lowercase_   )
																		UpperCAmelCase			 =					image.to(self.device   )
												else:
																		UpperCAmelCase			 =					randn_tensor(lowercase_  ,    generator=lowercase_  ,    device=self.device   )

												# set step values
												self.scheduler.set_timesteps(lowercase_   )

												for t in self.progress_bar(self.scheduler.timesteps   ):
																		# 1. predict noise model_output
																		UpperCAmelCase			 =					self.unet(lowercase_  ,    lowercase_   ).sample

																		# 2. compute previous image: x_t -> x_t-1
																		UpperCAmelCase			 =					self.scheduler.step(lowercase_  ,    lowercase_  ,    lowercase_  ,    generator=lowercase_   ).prev_sample

												UpperCAmelCase			 =					(image / 2 + 0.5).clamp(0  ,    1   )
												UpperCAmelCase			 =					image.cpu().permute(0  ,    2  ,    3  ,    1   ).numpy()
												if output_type == "pil":
																		UpperCAmelCase			 =					self.numpy_to_pil(lowercase_   )

												if not return_dict:
																		return (image,)

												return ImagePipelineOutput(images=lowercase_   )





