






'''simple docstring'''





import unittest
from timeit import timeit



def 			__UpperCAmelCase				(lowercase__	,lowercase__				)		->				int:

						'''simple docstring'''


						a_				     =   first_num if first_num >= second_num else second_num
						a_				     =   max_num
						while (common_mult % first_num > 0) or (common_mult % second_num > 0):
												common_mult += max_num
						return common_mult



def 			__UpperCAmelCase				(lowercase__	,lowercase__				)		->				int:

						'''simple docstring'''


						return b if a == 0 else greatest_common_divisor(b % a	,lowercase__				)



def 			__UpperCAmelCase				(lowercase__	,lowercase__				)		->				int:

						'''simple docstring'''


						return first_num // greatest_common_divisor(lowercase__	,lowercase__				) * second_num



def 			__UpperCAmelCase				()		->				Any:

						'''simple docstring'''


						a_				     =   (
						    "from __main__ import least_common_multiple_slow, least_common_multiple_fast"
						)
						print(
						    "least_common_multiple_slow():"	,timeit("least_common_multiple_slow(1000, 999)"	,setup=lowercase__				)	,)
						print(
						    "least_common_multiple_fast():"	,timeit("least_common_multiple_fast(1000, 999)"	,setup=lowercase__				)	,)





class 		SCREAMING_SNAKE_CASE__   (     unittest.TestCase    ):
		_UpperCAmelCase         =(
		    (10, 20),
		    (13, 15),
		    (4, 31),
		    (10, 42),
		    (43, 34),
		    (5, 12),
		    (12, 25),
		    (10, 25),
		    (6, 9),
		)
		_UpperCAmelCase         =(20, 195, 124, 210, 1462, 60, 300, 50, 18)



		def _lowerCAmelCase     (    self:    str)  ->int:






								'''simple docstring'''


								for i, (first_num, second_num) in enumerate(self.test_inputs):
														a_				     =   least_common_multiple_slow(a				,   a)
														a_				     =   least_common_multiple_fast(a				,   a)
														with self.subTest(i=a):
																				self.assertEqual(a				,   self.expected_results[i])
																				self.assertEqual(a				,   self.expected_results[i])


if __name__ == "__main__":
							benchmark()
							unittest.main()











'''simple docstring'''





from __future__ import annotations

a_      = [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]





class 		SCREAMING_SNAKE_CASE__   :



		def __init__(    self:    Optional[int]				,   a:    int)  ->None:






								'''simple docstring'''


								a_				     =   -1
								a_				     =   -1
								a_				     =   [-1] * length
								a_				     =   None
								a_				     =   None




		def __repr__(    self:    Union[str, Any])  ->str:






								'''simple docstring'''


								return f"""Node(min_value={self.minn} max_value={self.maxx})"""





def 			__UpperCAmelCase				(lowercase__				)		->				Node | None:

						'''simple docstring'''


						a_				     =   Node(len(lowercase__				)				)
						a_     ,       a_				     =   min(lowercase__				), max(lowercase__				)
						# Leaf node case where the node contains only one unique value
						if root.minn == root.maxx:
												return root
						a_				     =   (root.minn + root.maxx) // 2

						a_				     =   []
						a_				     =   []

						for index, num in enumerate(lowercase__				):
												if num <= pivot:
																		left_arr.append(lowercase__				)
												else:
																		right_arr.append(lowercase__				)
												a_				     =   len(lowercase__				)
						a_				     =   build_tree(lowercase__				)
						a_				     =   build_tree(lowercase__				)
						return root



def 			__UpperCAmelCase				(lowercase__	,lowercase__	,lowercase__				)		->				int:

						'''simple docstring'''


						if index < 0 or node is None:
												return 0
						# Leaf node cases
						if node.minn == node.maxx:
												return index + 1 if node.minn == num else 0
						a_				     =   (node.minn + node.maxx) // 2
						if num <= pivot:
												# go the left subtree and map index to the left subtree
												return rank_till_index(node.left	,lowercase__	,node.map_left[index] - 1				)
						else:
												# go to the right subtree and map index to the right subtree
												return rank_till_index(node.right	,lowercase__	,index - node.map_left[index]				)



def 			__UpperCAmelCase				(lowercase__	,lowercase__	,lowercase__	,lowercase__				)		->				int:

						'''simple docstring'''


						if start > end:
												return 0
						a_				     =   rank_till_index(lowercase__	,lowercase__	,lowercase__				)
						a_				     =   rank_till_index(lowercase__	,lowercase__	,start - 1				)
						return rank_till_end - rank_before_start



def 			__UpperCAmelCase				(lowercase__	,lowercase__	,lowercase__	,lowercase__				)		->				int:

						'''simple docstring'''


						if index > (end - start) or start > end or node is None:
												return -1
						# Leaf node case
						if node.minn == node.maxx:
												return node.minn
						# Number of elements in the left subtree in interval [start, end]
						a_				     =   node.map_left[end] - (
						    node.map_left[start - 1] if start else 0
						)
						if num_elements_in_left_tree > index:
												return quantile(
												    node.left	,lowercase__	,(node.map_left[start - 1] if start else 0)	,node.map_left[end] - 1	,)
						else:
												return quantile(
												    node.right	,index - num_elements_in_left_tree	,start - (node.map_left[start - 1] if start else 0)	,end - node.map_left[end]	,)



def 			__UpperCAmelCase				(lowercase__	,lowercase__	,lowercase__	,lowercase__	,lowercase__				)		->				int:

						'''simple docstring'''


						if (
						    start > end
						    or node is None
						    or start_num > end_num
						    or node.minn > end_num
						    or node.maxx < start_num
						):
												return 0
						if start_num <= node.minn and node.maxx <= end_num:
												return end - start + 1
						a_				     =   range_counting(
						    node.left	,(node.map_left[start - 1] if start else 0)	,node.map_left[end] - 1	,lowercase__	,lowercase__	,)
						a_				     =   range_counting(
						    node.right	,start - (node.map_left[start - 1] if start else 0)	,end - node.map_left[end]	,lowercase__	,lowercase__	,)
						return left + right


if __name__ == "__main__":
							import doctest

							doctest.testmod()



