def 					_snake_case	(  __snake_case  ,     __snake_case  ,     __snake_case						):


					if n == 0:
										return 1

					elif n % 2 == 1:
										return (binary_exponentiation(a__  ,     n - 1  ,     a__						) * a) % mod

					else:
										_UpperCamelCase			     =     binary_exponentiation(a__  ,     n / 2  ,     a__						)
										return (b * b) % mod


# a prime number
_lowerCAmelCase       =		701

_lowerCAmelCase       =		1_000_000_000
_lowerCAmelCase       =		10

# using binary exponentiation function, O(log(p)):
print((a / b) % p == (a * binary_exponentiation(b, p - 2, p)) % p)







print((a / b) % p == (a * b ** (p - 2)) % p)



'''simple docstring'''



import unittest

import numpy as np
import torch

from diffusers import KarrasVePipeline, KarrasVeScheduler, UNetaDModel
from diffusers.utils.testing_utils import enable_full_determinism, require_torch, slow, torch_device


enable_full_determinism()







class 		lowerCAmelCase__  ( unittest.TestCase   ):



 """simple docstring"""



 @property
 def  UpperCAmelCase__						(						self   :			int     )    ->					Optional[int]:


      """simple docstring"""




      torch.manual_seed(0     )
      __SCREAMING_SNAKE_CASE      = UNetaDModel(
          block_out_channels=(32, 64)   ,				layers_per_block=2   ,				sample_size=32   ,				in_channels=3   ,				out_channels=3   ,				down_block_types=("""DownBlock2D""", """AttnDownBlock2D""")   ,				up_block_types=("""AttnUpBlock2D""", """UpBlock2D""")   ,				)
      return model


 def  UpperCAmelCase__						(						self   :			Optional[Any]     )    ->					Tuple:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE      = self.dummy_uncond_unet
      __SCREAMING_SNAKE_CASE      = KarrasVeScheduler()

      __SCREAMING_SNAKE_CASE      = KarrasVePipeline(unet=__SCREAMING_SNAKE_CASE   ,				scheduler=__SCREAMING_SNAKE_CASE     )
      pipe.to(__SCREAMING_SNAKE_CASE     )
      pipe.set_progress_bar_config(disable=__SCREAMING_SNAKE_CASE     )

      __SCREAMING_SNAKE_CASE      = torch.manual_seed(0     )
      __SCREAMING_SNAKE_CASE      = pipe(num_inference_steps=2   ,				generator=__SCREAMING_SNAKE_CASE   ,				output_type="""numpy"""     ).images

      __SCREAMING_SNAKE_CASE      = torch.manual_seed(0     )
      __SCREAMING_SNAKE_CASE      = pipe(num_inference_steps=2   ,				generator=__SCREAMING_SNAKE_CASE   ,				output_type="""numpy"""   ,				return_dict=__SCREAMING_SNAKE_CASE     )[0]

      __SCREAMING_SNAKE_CASE      = image[0, -3:, -3:, -1]
      __SCREAMING_SNAKE_CASE      = image_from_tuple[0, -3:, -3:, -1]

      assert image.shape == (1, 32, 32, 3)
      __SCREAMING_SNAKE_CASE      = np.array([0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]     )

      assert np.abs(image_slice.flatten() - expected_slice     ).max() < 1E-2
      assert np.abs(image_from_tuple_slice.flatten() - expected_slice     ).max() < 1E-2







@slow
@require_torch
class 		lowerCAmelCase__  ( unittest.TestCase   ):



 """simple docstring"""



 def  UpperCAmelCase__						(						self   :			List[Any]     )    ->					Union[str, Any]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE      = """google/ncsnpp-celebahq-256"""
      __SCREAMING_SNAKE_CASE      = UNetaDModel.from_pretrained(__SCREAMING_SNAKE_CASE     )
      __SCREAMING_SNAKE_CASE      = KarrasVeScheduler()

      __SCREAMING_SNAKE_CASE      = KarrasVePipeline(unet=__SCREAMING_SNAKE_CASE   ,				scheduler=__SCREAMING_SNAKE_CASE     )
      pipe.to(__SCREAMING_SNAKE_CASE     )
      pipe.set_progress_bar_config(disable=__SCREAMING_SNAKE_CASE     )

      __SCREAMING_SNAKE_CASE      = torch.manual_seed(0     )
      __SCREAMING_SNAKE_CASE      = pipe(num_inference_steps=20   ,				generator=__SCREAMING_SNAKE_CASE   ,				output_type="""numpy"""     ).images

      __SCREAMING_SNAKE_CASE      = image[0, -3:, -3:, -1]
      assert image.shape == (1, 256, 256, 3)
      __SCREAMING_SNAKE_CASE      = np.array([0.578, 0.5811, 0.5924, 0.5809, 0.587, 0.5886, 0.5861, 0.5802, 0.586]     )

      assert np.abs(image_slice.flatten() - expected_slice     ).max() < 1E-2






