


"""simple docstring"""






def        lowerCamelCase_(		_lowerCamelCase			,		_lowerCamelCase       )    ->     int:
   '''simple docstring'''





   return abs(_lowerCamelCase       ) if a == 0 else greatest_common_divisor(b % a			,		_lowerCamelCase       )







def        lowerCamelCase_(		_lowerCamelCase			,		_lowerCamelCase       )    ->     int:
   '''simple docstring'''





   while y:  # --> when y=0 then loop will terminate and return x as final GCD.
      _lowerCamelCase,					_lowerCamelCase   :				Union[str, Any]							=     y, x % y
   return abs(_lowerCamelCase       )







def        lowerCamelCase_(		)    ->     str:
   '''simple docstring'''





   try:
      _lowerCamelCase   :				Any							=     input("Enter two integers separated by comma (,): "       ).split(","       )
      _lowerCamelCase   :				Dict							=     int(nums[0]       )
      _lowerCamelCase   :				Tuple							=     int(nums[1]       )
      print(
          F"""greatest_common_divisor({num_a}, {num_a}) = """
          F"""{greatest_common_divisor(_lowerCamelCase			,		_lowerCamelCase       )}"""       )
      print(F"""By iterative gcd({num_a}, {num_a}) = {gcd_by_iterative(_lowerCamelCase			,		_lowerCamelCase       )}"""       )
   except (IndexError, UnboundLocalError, ValueError):
      print("Wrong input"       )


if __name__ == "__main__":
  main()






from __future__ import annotations

import math



def 						A_							(	_lowerCAmelCase				,  _lowerCAmelCase	)		->					float:
 UpperCamelCase      :   Tuple			      =  u
 for i in range(1				,  _lowerCAmelCase	):
  UpperCamelCase      :   Any			      =  temp * (u - i)
 return temp



def 						A_							(	)		->					None:
 UpperCamelCase      :   Union[str, Any]			      =  int(input("enter the numbers of values: "	)	)
 UpperCamelCase      :   list[list[float]]			      =  []
 for _ in range(_lowerCAmelCase	):
  y.append([]	)
 for i in range(_lowerCAmelCase	):
  for j in range(_lowerCAmelCase	):
   y[i].append(_lowerCAmelCase	)
   UpperCamelCase      :   List[str]			      =  0

 print("enter the values of parameters in a list: "	)
 UpperCamelCase      :   Optional[Any]			      =  list(map(_lowerCAmelCase				,  input().split()	)	)

 print("enter the values of corresponding parameters: "	)
 for i in range(_lowerCAmelCase	):
  UpperCamelCase      :   Tuple			      =  float(input()	)

 UpperCamelCase      :   Any			      =  int(input("enter the value to interpolate: "	)	)
 UpperCamelCase      :   List[Any]			      =  (value - x[0]) / (x[1] - x[0])

 # for calculating forward difference table

 for i in range(1				,  _lowerCAmelCase	):
  for j in range(n - i	):
   UpperCamelCase      :   Optional[Any]			      =  y[j + 1][i - 1] - y[j][i - 1]

 UpperCamelCase      :   List[str]			      =  y[0][0]
 for i in range(1				,  _lowerCAmelCase	):
  summ += (ucal(_lowerCAmelCase				,  _lowerCAmelCase	) * y[0][i]) / math.factorial(_lowerCAmelCase	)

 print(F"""the value at {value} is {summ}"""	)


if __name__ == "__main__":
    main()
