



'''simple docstring'''





from __future__ import annotations




def 							lowerCamelCase	(					_snake_case	:    list[int]  ,_snake_case	:    int							):





    '''simple docstring'''


    lowercase__									=    0
    lowercase__									=    len(_snake_case							) - 1

    while i < j:
        if nums[i] + nums[j] == target:
            return [i, j]
        elif nums[i] + nums[j] < target:
            lowercase__									=    i + 1
        else:
            lowercase__									=    j - 1

    return []


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(f'''{two_pointer([2, 7, 11, 15], 9) = }''')









'''simple docstring'''





from __future__ import annotations




def 							lowerCamelCase	(					_snake_case	:    int  ,_snake_case	:    int							):





    '''simple docstring'''


    if b == 0:
        return (1, 0)
    ((lowercase__)							,							(lowercase__))									=    extended_euclid(_snake_case  ,a % b							)
    lowercase__									=    a // b
    return (y, x - k * y)




def 							lowerCamelCase	(					_snake_case	:    int  ,_snake_case	:    int  ,_snake_case	:    int  ,_snake_case	:    int							):





    '''simple docstring'''


    ((lowercase__)							,							(lowercase__))									=    extended_euclid(_snake_case  ,_snake_case							)
    lowercase__									=    na * na
    lowercase__									=    ra * x * na + ra * y * na
    return (n % m + m) % m




def 							lowerCamelCase	(					_snake_case	:    int  ,_snake_case	:    int							):





    '''simple docstring'''


    ((lowercase__)							,							(lowercase__))									=    extended_euclid(_snake_case  ,_snake_case							)
    if b < 0:
        lowercase__									=    (b % n + n) % n
    return b




def 							lowerCamelCase	(					_snake_case	:    int  ,_snake_case	:    int  ,_snake_case	:    int  ,_snake_case	:    int							):





    '''simple docstring'''


    lowercase__							,							lowercase__									=    invert_modulo(_snake_case  ,_snake_case							), invert_modulo(_snake_case  ,_snake_case							)
    lowercase__									=    na * na
    lowercase__									=    ra * x * na + ra * y * na
    return (n % m + m) % m


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

 testmod(name="chinese_remainder_theorem", verbose=True)
 testmod(name="chinese_remainder_theorem2", verbose=True)
 testmod(name="invert_modulo", verbose=True)
 testmod(name="extended_euclid", verbose=True)




