code: '''simple docstring'''
  
  
  
  
  
  from __future__ import annotations
  def 				__lowercase	(						lowerCamelCase__ ,				lowerCamelCase__ ,				lowerCamelCase__					)				->tuple[float, float]:
  
    '''simple docstring'''
  
  
  
  
    assert (
        c % greatest_common_divisor(SCREAMING_SNAKE_CASE__ ,				SCREAMING_SNAKE_CASE__					) == 0
    )  # greatest_common_divisor(a,b) function implemented below
    (a__)     		=     extended_gcd(SCREAMING_SNAKE_CASE__ ,				SCREAMING_SNAKE_CASE__					)  # extended_gcd(a,b) function implemented below
    a__     		=     c / d
    return (r * x, r * y)
  def 				__lowercase	(						lowerCamelCase__ ,				lowerCamelCase__ ,				lowerCamelCase__ ,				lowerCamelCase__ = 2					)				->None:
  
    '''simple docstring'''
  
  
  
  
    (a__)     		=     diophantine(SCREAMING_SNAKE_CASE__ ,				SCREAMING_SNAKE_CASE__ ,				SCREAMING_SNAKE_CASE__					)  # Initial value
    a__     		=     greatest_common_divisor(SCREAMING_SNAKE_CASE__ ,				SCREAMING_SNAKE_CASE__					)
    a__     		=     a // d
    a__     		=     b // d
  
    for i in range(SCREAMING_SNAKE_CASE__					):
      a__     		=     xa + i * q
      a__     		=     ya - i * p
      print(SCREAMING_SNAKE_CASE__ ,				SCREAMING_SNAKE_CASE__					)
  def 				__lowercase	(						lowerCamelCase__ ,				lowerCamelCase__					)				->int:
  
    '''simple docstring'''
  
  
  
  
    if a < b:
      a__     		=     b, a
  
    while a % b != 0:
      a__     		=     b, a % b
  
    return b
  def 				__lowercase	(						lowerCamelCase__ ,				lowerCamelCase__					)				->tuple[int, int, int]:
  
    '''simple docstring'''
  
  
  
  
    assert a >= 0 and b >= 0
  
    if b == 0:
      a__     		=     a, 1, 0
    else:
      (a__)     		=     extended_gcd(SCREAMING_SNAKE_CASE__ ,				a % b					)
      a__     		=     q
      a__     		=     p - q * (a // b)
  
    assert a % d == 0 and b % d == 0
    assert d == a * x + b * y
  
    return (d, x, y)
  
  
  if __name__ == "__main__":
       from doctest import testmod
  
       testmod(name="""diophantine""", verbose=True)
       testmod(name="""diophantine_all_soln""", verbose=True)
       testmod(name="""extended_gcd""", verbose=True)
       testmod(name="""greatest_common_divisor""", verbose=True)
  
  
style_context: def 				__lowercase	(						lowerCamelCase__ ,				lowerCamelCase__					)				->Optional[int]:
  
    '''simple docstring'''
  
  
  
  
    sequence.append(lowerCamelCase__					)
  
    a__     		=     0
    while sequence[index] != target:
      index += 1
  
    sequence.pop()
  
    if index == len(lowerCamelCase__					):
      return None
  
    return index
  
  
  if __name__ == "__main__":
       _SCREAMING_SNAKE_CASE   						=    input("""Enter numbers separated by comma:\n""").strip()
       _SCREAMING_SNAKE_CASE   						=    [int(item) for item in user_input.split(""",""")]
  
       _SCREAMING_SNAKE_CASE   						=    input("""Enter a single number to be found in the list:\n""")
       _SCREAMING_SNAKE_CASE   						=    int(target_input)
       _SCREAMING_SNAKE_CASE   						=    sentinel_linear_search(sequence, target)
       if result is not None:
            print(F"""{target} found at positions: {result}""")
       else:
            print("""Not found""")
  
  