



"""simple docstring"""





def   a__      ( lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__ ):
      if n == 0:
            return 1

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

      else:
            UpperCAmelCase_     					=				binary_exponentiation(lowerCAmelCase__      ,     n / 2      ,     lowerCAmelCase__ )
            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)











import unittest
from dataclasses import dataclass

import pytest

from accelerate.commands.config.config_args import SageMakerConfig
from accelerate.utils import ComputeEnvironment
from accelerate.utils.launch import _convert_nargs_to_dict




@dataclass
class        SCREAMING_SNAKE_CASE__					(		UpperCamelCase__ ):
 __SCREAMING_SNAKE_CASE							=      ComputeEnvironment.AMAZON_SAGEMAKER
 __SCREAMING_SNAKE_CASE							=      True
 __SCREAMING_SNAKE_CASE							=      '''ml.p3.2xlarge'''
 __SCREAMING_SNAKE_CASE							=      '''accelerate_sagemaker_execution_role'''
 __SCREAMING_SNAKE_CASE							=      '''hf-sm'''
 __SCREAMING_SNAKE_CASE							=      '''us-east-1'''
 __SCREAMING_SNAKE_CASE							=      1
 __SCREAMING_SNAKE_CASE							=      '''accelerate-sagemaker-1'''
 __SCREAMING_SNAKE_CASE							=      '''1.6'''
 __SCREAMING_SNAKE_CASE							=      '''4.4'''
 __SCREAMING_SNAKE_CASE							=      '''train.py'''
 __SCREAMING_SNAKE_CASE							=      [
     '''--model_name_or_path''',
     '''bert''',
     '''--do_train''',
     '''False''',
     '''--epochs''',
     '''3''',
     '''--learning_rate''',
     '''5e-5''',
     '''--max_steps''',
     '''50.5''',
 ]
 __SCREAMING_SNAKE_CASE							=      [
     '''--model_name_or_path''',
     '''bert''',
     '''--do_train''',
     '''--do_test''',
     '''False''',
     '''--do_predict''',
     '''--epochs''',
     '''3''',
     '''--learning_rate''',
     '''5e-5''',
     '''--max_steps''',
     '''50.5''',
 ]




class        SCREAMING_SNAKE_CASE__					(		unittest.TestCase ):



 def 							UpperCamelCase     (				self					):
        # If no defaults are changed, `to_kwargs` returns an empty dict.
        A__		   =		_convert_nargs_to_dict(MockLaunchConfig.success_training_script_args					)
        assert isinstance(converted_args['''model_name_or_path'''],__lowerCamelCase					)
        assert isinstance(converted_args['''do_train'''],__lowerCamelCase					)
        assert isinstance(converted_args['''epochs'''],__lowerCamelCase					)
        assert isinstance(converted_args['''learning_rate'''],__lowerCamelCase					)
        assert isinstance(converted_args['''max_steps'''],__lowerCamelCase					)

        with pytest.raises(__lowerCamelCase					):
               _convert_nargs_to_dict(MockLaunchConfig.fail_training_script_args					)





