



import numpy as np






def 					__lowerCAmelCase		(  __lowerCamelCase	:    np.array	)  ->						np.array:
					return 1 / (1 + np.exp(-vector	))


if __name__ == "__main__":
				import doctest

				doctest.testmod()









def 					__lowerCAmelCase		(  __lowerCamelCase	:    int = 3				,   __lowerCamelCase	:    int = 7				,   __lowerCamelCase	:    int = 1000000	)  ->						int:
					__lowerCAmelCase	   =0
					__lowerCAmelCase	   =1

					for current_denominator in range(1				,   limit + 1	):
										__lowerCAmelCase	   =current_denominator * numerator // denominator
										if current_denominator % denominator == 0:
															current_numerator -= 1
										if current_numerator * max_denominator > current_denominator * max_numerator:
															__lowerCAmelCase	   =current_numerator
															__lowerCAmelCase	   =current_denominator
					return max_numerator


if __name__ == "__main__":
				print(solution(numerator=3, denominator=7, limit=1_00_00_00))




