code: from __future__ import annotations
  def 				__lowercase	(						lowerCamelCase__ ,				lowerCamelCase__ ,				lowerCamelCase__					)				->tuple[float, float]:
  
    '''simple docstring'''
  
  
  
  
    assert (
        c % greatest_common_divisor(lowerCamelCase__ ,				lowerCamelCase__					) == 0
    )  # greatest_common_divisor(a,b) function implemented below
    ((a__)		,(a__)		,(a__))     		=     extended_gcd(lowerCamelCase__ ,				lowerCamelCase__					)  # 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__)		,(a__))     		=     diophantine(lowerCamelCase__ ,				lowerCamelCase__ ,				lowerCamelCase__					)  # Initial value
    a__     		=     greatest_common_divisor(lowerCamelCase__ ,				lowerCamelCase__					)
    a__     		=     a // d
    a__     		=     b // d
  
    for i in range(lowerCamelCase__					):
      a__     		=     xa + i * q
      a__     		=     ya - i * p
      print(lowerCamelCase__ ,				lowerCamelCase__					)
  def 				__lowercase	(						lowerCamelCase__ ,				lowerCamelCase__					)				->int:
  
    '''simple docstring'''
  
  
  
  
    if a < b:
      a__		,a__     		=     b, a
  
    while a % b != 0:
      a__		,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__		,a__     		=     a, 1, 0
    else:
      ((a__)		,(a__)		,(a__))     		=     extended_gcd(lowerCamelCase__ ,				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: from unittest.mock import patch
  
  import datasets
  from datasets import Dataset
  def 				__lowercase	(						)				->Union[str, Any]:
  
    '''simple docstring'''
  
  
  
  
    a__     		=     Dataset.from_dict({"col_1": [3, 2, 0, 1]}					)
  
    with patch("tqdm.auto.tqdm"					) as mock_tqdm:
      datasets.disable_progress_bar()
      dset.map(lambda lowerCamelCase__					: {"col_2": x["col_1"] + 1}					)
      mock_tqdm.assert_not_called()
  
      mock_tqdm.reset_mock()
  
      datasets.enable_progress_bar()
      dset.map(lambda lowerCamelCase__					: {"col_2": x["col_1"] + 1}					)
      mock_tqdm.assert_called()
  
  