






from __future__ import annotations





def 					snake_case	(  lowerCamelCase					,	lowerCamelCase       ):




	'''simple docstring'''







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





def 					snake_case	(  lowerCamelCase					,	lowerCamelCase					,	lowerCamelCase					,	lowerCamelCase       ):




	'''simple docstring'''







	((__lowercase)							,    (__lowercase))   							=	extended_euclid(lowerCamelCase					,	lowerCamelCase       )
	__lowercase   							=	na * na
	__lowercase   							=	ra * x * na + ra * y * na
	return (n % m + m) % m





def 					snake_case	(  lowerCamelCase					,	lowerCamelCase       ):




	'''simple docstring'''







	((__lowercase)							,    (__lowercase))   							=	extended_euclid(lowerCamelCase					,	lowerCamelCase       )
	if b < 0:
		__lowercase   							=	(b % n + n) % n
	return b





def 					snake_case	(  lowerCamelCase					,	lowerCamelCase					,	lowerCamelCase					,	lowerCamelCase       ):




	'''simple docstring'''







	__lowercase							,    __lowercase   							=	invert_modulo(lowerCamelCase					,	lowerCamelCase       ), invert_modulo(lowerCamelCase					,	lowerCamelCase       )
	__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)





'''simple docstring'''

from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass
@dataclass
class     __lowerCAmelCase		:





      '''simple docstring'''






      lowerCAmelCase__   :	int
      lowerCAmelCase__   :	TreeNode | None       =				None
      lowerCAmelCase__   :	TreeNode | None       =				None






lowerCamelCase				:  Optional[Any]    		=      namedtuple('CoinsDistribResult', 'moves excess')

def _SCREAMING_SNAKE_CASE (A			)			->			int:






       """simple docstring"""







       if root is None:
              return 0

       # Validation
       def count_nodes(A			) -> int:
              if node is None:
                     return 0

              return count_nodes(node.left			) + count_nodes(node.right			) + 1

       def count_coins(A			) -> int:
              if node is None:
                     return 0

              return count_coins(node.left			) + count_coins(node.right			) + node.data

       if count_nodes(A			) != count_coins(A			):
              raise ValueError('''The nodes number should be same as the number of coins'''			)

       # Main calculation
       def get_distrib(A			) -> CoinsDistribResult:

              if node is None:
                     return CoinsDistribResult(0    ,					1			)

              lowercase__     ,lowercase__      =					get_distrib(node.left			)
              lowercase__     ,lowercase__      =					get_distrib(node.right			)

              lowercase__      =					1 - left_distrib_excess
              lowercase__      =					1 - right_distrib_excess

              lowercase__      =					(
                  left_distrib_moves
                  + right_distrib_moves
                  + abs(A			)
                  + abs(A			)
              )
              lowercase__      =					node.data - coins_to_left - coins_to_right

              return CoinsDistribResult(A    ,					A			)

       return get_distrib(A			)[0]


if __name__ == "__main__":
 import doctest

 doctest.testmod()




