



def      _A				(UpperCamelCase		:      List[Any]      ,			UpperCamelCase		:      Dict )  ->List[str]:



			'''simple docstring'''







			lowerCamelCase__ :      int								=		[1]
			for i in range(2      ,			UpperCamelCase ):
						factorials.append(factorials[-1] * i )
			assert 0 <= k < factorials[-1] * n, "k out of bounds"

			lowerCamelCase__ :      Union[str, Any]								=		[]
			lowerCamelCase__ :      Optional[Any]								=		list(range(UpperCamelCase ) )

			# Find permutation
			while factorials:
						lowerCamelCase__ :      Union[str, Any]								=		factorials.pop()
						lowerCamelCase__							,lowerCamelCase__ :      Union[str, Any]								=		divmod(UpperCamelCase      ,			UpperCamelCase )
						permutation.append(elements[number] )
						elements.remove(elements[number] )
			permutation.append(elements[0] )

			return permutation


if __name__ == "__main__":
				import doctest

				doctest.testmod()








def      _A				(UpperCamelCase		:      int      ,			UpperCamelCase		:      int )  ->int:



			'''simple docstring'''







			while b:
						lowerCamelCase__							,lowerCamelCase__ :      int								=		b, a % b
			return a






def      _A				(UpperCamelCase		:      int      ,			UpperCamelCase		:      int )  ->int:



			'''simple docstring'''







			return a if b == 0 else euclidean_gcd_recursive(UpperCamelCase      ,			a % b )






def      _A				()  ->str:



			'''simple docstring'''







			print(f"euclidean_gcd(3, 5) = {euclidean_gcd(3      ,			5 )}" )
			print(f"euclidean_gcd(5, 3) = {euclidean_gcd(5      ,			3 )}" )
			print(f"euclidean_gcd(1, 3) = {euclidean_gcd(1      ,			3 )}" )
			print(f"euclidean_gcd(3, 6) = {euclidean_gcd(3      ,			6 )}" )
			print(f"euclidean_gcd(6, 3) = {euclidean_gcd(6      ,			3 )}" )

			print(f"euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3      ,			5 )}" )
			print(f"euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5      ,			3 )}" )
			print(f"euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1      ,			3 )}" )
			print(f"euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3      ,			6 )}" )
			print(f"euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6      ,			3 )}" )


if __name__ == "__main__":
				main()



