
'''simple docstring'''

def 						_UpperCAmelCase					(	_lowerCamelCase    :							Union[str, Any]	,   _lowerCamelCase    :							List[str]	,   _lowerCamelCase    :							str		)     ->    Optional[int]:


  if n == 0:
    return 1

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

  else:
    _lowerCAmelCase							:	Dict 					=       binary_exponentiation(SCREAMING_SNAKE_CASE__	,   n / 2	,   SCREAMING_SNAKE_CASE__		)
    return (b * b) % mod


# a prime number
UpperCamelCase_        =							7_01

UpperCamelCase_        =							10_00_00_00_00
UpperCamelCase_        =							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 numpy as np




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__			)  ->							np.ndarray:


		'''simple docstring'''


		return 1 / (1 + np.exp(-vector			))




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__			)  ->							np.ndarray:


		'''simple docstring'''


		return vector * sigmoid(SCREAMING_SNAKE_CASE__			)


if __name__ == "__main__":
						import doctest

						doctest.testmod()


