




'''simple docstring'''





from __future__ import annotations





def UpperCAmelCase						(					UpperCAmelCase_      ,  UpperCAmelCase_      ,  UpperCAmelCase_	):
    assert n > 1 and a > 0 and greatest_common_divisor(UpperCAmelCase_      ,  UpperCAmelCase_	) == 1
    (_a)							:       List[str]       					=			extended_gcd(UpperCAmelCase_      ,  UpperCAmelCase_	)  # Implemented below
    _a							:       List[Any]       					=			(b * s) % n
    return x





def UpperCAmelCase						(					UpperCAmelCase_      ,  UpperCAmelCase_	):
    (_a)							:       List[str]       					=			extended_euclid(UpperCAmelCase_      ,  UpperCAmelCase_	)  # Implemented below
    if b < 0:
        _a							:       Tuple       					=			(b % n + n) % n
    return b





def UpperCAmelCase						(					UpperCAmelCase_      ,  UpperCAmelCase_      ,  UpperCAmelCase_	):
    _a							:       Tuple       					=			invert_modulo(UpperCAmelCase_      ,  UpperCAmelCase_	)
    _a							:       List[str]       					=			(b * s) % n
    return x





def UpperCAmelCase						(					UpperCAmelCase_      ,  UpperCAmelCase_	):
    assert a >= 0 and b >= 0

    if b == 0:
        _a							:       Dict       					=			a, 1, 0
    else:
        (_a)							:       Any       					=			extended_gcd(UpperCAmelCase_      ,  a % b	)
        _a							:       List[Any]       					=			q
        _a							:       List[str]       					=			p - q * (a // b)

    assert a % d == 0 and b % d == 0
    assert d == a * x + b * y

    return (d, x, y)





def UpperCAmelCase						(					UpperCAmelCase_      ,  UpperCAmelCase_	):
    if b == 0:
        return (1, 0)
    (_a)							:       Union[str, Any]       					=			extended_euclid(UpperCAmelCase_      ,  a % b	)
    _a							:       Optional[int]       					=			a // b
    return (y, x - k * y)





def UpperCAmelCase						(					UpperCAmelCase_      ,  UpperCAmelCase_	):
    if a < b:
        _a							:       List[Any]       					=			b, a

    while a % b != 0:
        _a							:       Dict       					=			b, a % b

    return b


if __name__ == "__main__":
  from doctest import testmod

  testmod(name='''modular_division''', verbose=True)
  testmod(name='''modular_division2''', verbose=True)
  testmod(name='''invert_modulo''', verbose=True)
  testmod(name='''extended_gcd''', verbose=True)
  testmod(name='''extended_euclid''', verbose=True)
  testmod(name='''greatest_common_divisor''', verbose=True)








'''simple docstring'''





from math import exp





def UpperCAmelCase						(					UpperCAmelCase_	):
    return 8 * x - 2 * exp(-x	)





def UpperCAmelCase						(					UpperCAmelCase_      ,  UpperCAmelCase_      ,  UpperCAmelCase_	):
    _a							:       Optional[int]       					=			lower_bound
    _a							:       str       					=			upper_bound
    for _ in range(0      ,  UpperCAmelCase_	):
        _a					,   _a							:       List[str]       					=			xa, xa - (f(UpperCAmelCase_	) * (xa - xa)) / (f(UpperCAmelCase_	) - f(UpperCAmelCase_	))
    return xa


if __name__ == "__main__":
  print(F"""Example: {secant_method(1, 3, 2)}""")


