The power of an integer x is defined as the number of steps needed to transform x into 1 using the following steps:

if x is even then x = x / 2
if x is odd then x = 3 * x + 1

For example, the power of x = 3 is 7 because 3 needs 7 steps to become 1 (3 --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1).
Given three integers lo, hi and k. The task is to sort all integers in the interval [lo, hi] by the power value in ascending order, if two or more integers have the same power value sort them by ascending order.
Return the k-th integer in the range [lo, hi] sorted by the power value.
Notice that for any integer x (lo <= x <= hi) it is guaranteed that x will transform into 1 using these steps and that the power of x is will fit in 32 bit signed integer.
 
Example 1:
Input: lo = 12, hi = 15, k = 2
Output: 13
Explanation: The power of 12 is 9 (12 --> 6 --> 3 --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1)
The power of 13 is 9
The power of 14 is 17
The power of 15 is 17
The interval sorted by the power value [12,13,14,15]. For k = 2 answer is the second element which is 13.
Notice that 12 and 13 have the same power value and we sorted them in ascending order. Same for 14 and 15.

Example 2:
Input: lo = 1, hi = 1, k = 1
Output: 1

Example 3:
Input: lo = 7, hi = 11, k = 4
Output: 7
Explanation: The power array corresponding to the interval [7, 8, 9, 10, 11] is [16, 3, 19, 6, 14].
The interval sorted by power is [8, 10, 11, 7, 9].
The fourth number in the sorted array is 7.

Example 4:
Input: lo = 10, hi = 20, k = 5
Output: 13

Example 5:
Input: lo = 1, hi = 1000, k = 777
Output: 570

 
Constraints:

1 <= lo <= hi <= 1000
1 <= k <= hi - lo + 1

Difficulty: MEDIUM
Starter code: class Solution:
    def getKth(self, lo: int, hi: int, k: int) -> int:
        

Solutions:
class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		return sorted(range(lo, hi + 1), key='寒寒寓寙寔寗寚寢寕寥寘寠寛寛寣寣寖寞實實寙寙寡寡寜審寜屁寤寤寤尼寗寬察察寧寧寧寴寚尿寚寯寢寢寢尺寝寪寪寪寝寝层层寥寲寥寲寥寥尽尽寘寭寭寭寠寠寠尸寨居寨寠寨寨寵寵寛寨局局寛寛寰寰寣寰寣尮寣寣尻尻寞屈寫寫寫寫寫尩寞寸寞尶屃屃屃尗實寞寳寳實實寳寳實就實尀尾尾尾尀寙屋寮寮寮寮寮寻寡尬寡寻寡寡尹尹審屆屆屆審審寡寡審寶審尧寶寶寶專寜尴審審屁屁屁尕寜尃寜屎寱寱寱尢寤寱寱寱寤寤尯尯寤対寤対尼尼尼対察屉屉屉寬寬寬屉寬寤寬对寬寬尪尪察对对对察察尷尷屄寬屄将屄屄尘尘寧将察察寴寴寴屑寧尥寧屑寴寴寴将寧寧尲尲寧寧封封尿封尿尓尿尿封封寚屌屌屌寯寯寯尠寯屌寯寧寯寯导导寢寯尭尭寢寢导导寢导寢導尺尺尺导寪寯屇屇屇屇屇尉寪尛寪屇寢寢寢导寪寷寷寷寪寪尨尨寷屔寷寷寷寷尉尉寝寪尵尵寪寪寪屡层射层寪层层尖尖寝层射射寝寝屏屏寲屏寲屏寲寲尣尣寥屏寲寲寲寲寲射寥寿寥寿尰尰尰寿寥寥寿寿寥寥寿寿尽少尽尌尽尽寿寿寠寲届届届届届届寭尌寭尞寭寭届届寭寥寥寥寭寭寺寺寭寺寭屗尫尫尫屗寠屗寺寺寺寺寺寲寠尌寠將尸尸尸寺居寭寭寭居居將將居寭居將尙尙尙尳寨居將將寠寠寠寺寵屒寵屒寵寵屒屒寨寵尦尦寨寨屒屒寵寵寵寭寵寵將將寨専寨寨尳尳尳屟寨専寨屟専専専尳局寨専専局局尔尔局小局寵専専専小寛寵屍屍屍屍屍小寰屍寰屍寰寰尡尡寰寰屍屍寰寰寨寨寰寨寰専寽寽寽屚寣寽寰寰尮尮尮寽寣屚寣寰寽寽寽尩寣寽寽寽寣寣小小尻尊尻寰尻尻寽寽寫寰寰寰屈屈屈寰屈尊屈屈屈屈尊尊寫尜尜尜寫寫屈屈寣尊寣尗寣寣寽寽寫展寸寸寸寸寸尗寫展寫展尩尩尩展寸寫展展寸寸寸寸寸寰寸寰尊尊尊展寞尅寫寫尶尶尶寸寫屢寫尶寫寫屢屢屃尅尅尅屃屃寫寫屃尅屃屢尗尗尗就寞尒屃屃尅尅尅尒寞尒寞寸屐屐屐寸寳屐屐屐寳寳屐屐寳屐寳尒尤尤尤屼實寳屐屐寳寳寳尒寳寫寳寫寳寳尅尅實尀尀尀實實尀尀就寳就屝就就尀尀實屝實實尀尀尀就實尬實尀尀尀尀屝尾實尒尒尾尾對對尾寳尾屪尀尀尀對寡寳寳寳屋屋屋屪屋寳屋對屋屋屋屋寮屋對對寮寮尟尟寮尟寮尹屋屋屋尚寮對實實實實實尚寮尀寮屘寻寻寻屘寮寻寻寻寮寮屘屘尬屘尬寻尬尬屘屘寡寮屘屘寻寻寻尧寻寻寻寻寻寻寳寳寡對對對寡寡專專尹寮尹履尹尹寻寻屆履寮寮寮寮寮岄屆履屆寮專專專履屆屆寮寮屆屆專專尚履尚尀尚尚尴尴審尕屆屆專專專屆寡尕寡專寡寡寻寻寶屓屓屓寶寶屓屓寶屓寶尕屓屓屓屆審屓寶寶尧尧尧屓審屿審尧屓屓屓寶寶寶寶寶寶寶寮寮寶寮寶寮專專專屓審尃尃尃審審審屠尴尃尴寶尴尴屠屠審尴尃尃審審屠屠尃審尃寶尃尃尴尴屁尯審審尃尃尃尃屁'.__getitem__)[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		return sorted(list(range(lo, hi + 1)), key=[1, 1, 2, 8, 3, 6, 9, 17, 4, 20, 7, 15, 10, 10, 18, 18, 5, 13, 21, 21, 8, 8, 16, 16, 11, 24, 11, 112, 19, 19, 19, 107, 6, 27, 14, 14, 22, 22, 22, 35, 9, 110, 9, 30, 17, 17, 17, 105, 12, 25, 25, 25, 12, 12, 113, 113, 20, 33, 20, 33, 20, 20, 108, 108, 7, 28, 28, 28, 15, 15, 15, 103, 23, 116, 23, 15, 23, 23, 36, 36, 10, 23, 111, 111, 10, 10, 31, 31, 18, 31, 18, 93, 18, 18, 106, 106, 13, 119, 26, 26, 26, 26, 26, 88, 13, 39, 13, 101, 114, 114, 114, 70, 21, 13, 34, 34, 21, 21, 34, 34, 21, 96, 21, 47, 109, 109, 109, 47, 8, 122, 29, 29, 29, 29, 29, 42, 16, 91, 16, 42, 16, 16, 104, 104, 24, 117, 117, 117, 24, 24, 16, 16, 24, 37, 24, 86, 37, 37, 37, 55, 11, 99, 24, 24, 112, 112, 112, 68, 11, 50, 11, 125, 32, 32, 32, 81, 19, 32, 32, 32, 19, 19, 94, 94, 19, 45, 19, 45, 107, 107, 107, 45, 14, 120, 120, 120, 27, 27, 27, 120, 27, 19, 27, 40, 27, 27, 89, 89, 14, 40, 40, 40, 14, 14, 102, 102, 115, 27, 115, 53, 115, 115, 71, 71, 22, 53, 14, 14, 35, 35, 35, 128, 22, 84, 22, 128, 35, 35, 35, 53, 22, 22, 97, 97, 22, 22, 48, 48, 110, 48, 110, 66, 110, 110, 48, 48, 9, 123, 123, 123, 30, 30, 30, 79, 30, 123, 30, 22, 30, 30, 43, 43, 17, 30, 92, 92, 17, 17, 43, 43, 17, 43, 17, 61, 105, 105, 105, 43, 25, 30, 118, 118, 118, 118, 118, 56, 25, 74, 25, 118, 17, 17, 17, 43, 25, 38, 38, 38, 25, 25, 87, 87, 38, 131, 38, 38, 38, 38, 56, 56, 12, 25, 100, 100, 25, 25, 25, 144, 113, 51, 113, 25, 113, 113, 69, 69, 12, 113, 51, 51, 12, 12, 126, 126, 33, 126, 33, 126, 33, 33, 82, 82, 20, 126, 33, 33, 33, 33, 33, 51, 20, 46, 20, 46, 95, 95, 95, 46, 20, 20, 46, 46, 20, 20, 46, 46, 108, 64, 108, 59, 108, 108, 46, 46, 15, 33, 121, 121, 121, 121, 121, 121, 28, 59, 28, 77, 28, 28, 121, 121, 28, 20, 20, 20, 28, 28, 41, 41, 28, 41, 28, 134, 90, 90, 90, 134, 15, 134, 41, 41, 41, 41, 41, 33, 15, 59, 15, 54, 103, 103, 103, 41, 116, 28, 28, 28, 116, 116, 54, 54, 116, 28, 116, 54, 72, 72, 72, 98, 23, 116, 54, 54, 15, 15, 15, 41, 36, 129, 36, 129, 36, 36, 129, 129, 23, 36, 85, 85, 23, 23, 129, 129, 36, 36, 36, 28, 36, 36, 54, 54, 23, 49, 23, 23, 98, 98, 98, 142, 23, 49, 23, 142, 49, 49, 49, 98, 111, 23, 49, 49, 111, 111, 67, 67, 111, 62, 111, 36, 49, 49, 49, 62, 10, 36, 124, 124, 124, 124, 124, 62, 31, 124, 31, 124, 31, 31, 80, 80, 31, 31, 124, 124, 31, 31, 23, 23, 31, 23, 31, 49, 44, 44, 44, 137, 18, 44, 31, 31, 93, 93, 93, 44, 18, 137, 18, 31, 44, 44, 44, 88, 18, 44, 44, 44, 18, 18, 62, 62, 106, 57, 106, 31, 106, 106, 44, 44, 26, 31, 31, 31, 119, 119, 119, 31, 119, 57, 119, 119, 119, 119, 57, 57, 26, 75, 75, 75, 26, 26, 119, 119, 18, 57, 18, 70, 18, 18, 44, 44, 26, 132, 39, 39, 39, 39, 39, 70, 26, 132, 26, 132, 88, 88, 88, 132, 39, 26, 132, 132, 39, 39, 39, 39, 39, 31, 39, 31, 57, 57, 57, 132, 13, 52, 26, 26, 101, 101, 101, 39, 26, 145, 26, 101, 26, 26, 145, 145, 114, 52, 52, 52, 114, 114, 26, 26, 114, 52, 114, 145, 70, 70, 70, 96, 13, 65, 114, 114, 52, 52, 52, 65, 13, 65, 13, 39, 127, 127, 127, 39, 34, 127, 127, 127, 34, 34, 127, 127, 34, 127, 34, 65, 83, 83, 83, 171, 21, 34, 127, 127, 34, 34, 34, 65, 34, 26, 34, 26, 34, 34, 52, 52, 21, 47, 47, 47, 21, 21, 47, 47, 96, 34, 96, 140, 96, 96, 47, 47, 21, 140, 21, 21, 47, 47, 47, 96, 21, 91, 21, 47, 47, 47, 47, 140, 109, 21, 65, 65, 109, 109, 60, 60, 109, 34, 109, 153, 47, 47, 47, 60, 16, 34, 34, 34, 122, 122, 122, 153, 122, 34, 122, 60, 122, 122, 122, 122, 29, 122, 60, 60, 29, 29, 78, 78, 29, 78, 29, 104, 122, 122, 122, 73, 29, 60, 21, 21, 21, 21, 21, 73, 29, 47, 29, 135, 42, 42, 42, 135, 29, 42, 42, 42, 29, 29, 135, 135, 91, 135, 91, 42, 91, 91, 135, 135, 16, 29, 135, 135, 42, 42, 42, 86, 42, 42, 42, 42, 42, 42, 34, 34, 16, 60, 60, 60, 16, 16, 55, 55, 104, 29, 104, 148, 104, 104, 42, 42, 117, 148, 29, 29, 29, 29, 29, 179, 117, 148, 117, 29, 55, 55, 55, 148, 117, 117, 29, 29, 117, 117, 55, 55, 73, 148, 73, 47, 73, 73, 99, 99, 24, 68, 117, 117, 55, 55, 55, 117, 16, 68, 16, 55, 16, 16, 42, 42, 37, 130, 130, 130, 37, 37, 130, 130, 37, 130, 37, 68, 130, 130, 130, 117, 24, 130, 37, 37, 86, 86, 86, 130, 24, 174, 24, 86, 130, 130, 130, 37, 37, 37, 37, 37, 37, 37, 29, 29, 37, 29, 37, 29, 55, 55, 55, 130, 24, 50, 50, 50, 24, 24, 24, 143, 99, 50, 99, 37, 99, 99, 143, 143, 24, 99, 50, 50, 24, 24, 143, 143, 50, 24, 50, 37, 50, 50, 99, 99, 112, 94, 24, 24, 50, 50, 50, 50, 112].__getitem__)[k - 1]


from heapq import heappush, heappop

class Solution:
	dp = {}

	def getKth(self, lo: int, hi: int, k: int) -> int:
		heap = []
		for i in range(lo, hi + 1):
			heappush(heap, [self.getPower(i), i])
		if len(heap) < k:
			return -1
		result = heappop(heap)
		for i in range(1, k):
			result = heappop(heap)
		return result[1]

	def getPower(self, n: int) -> int:
		if n == 1:
			return 1
		if n in self.dp:
			return self.dp[n]
		result = 0
		if n % 2 == 0:
			result = 1 + self.getPower(n // 2)
		else:
			result = 1 + self.getPower(n * 3 + 1)
		self.dp[n] = result
		return result


from functools import lru_cache

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		res = []
		for i in range(lo, hi + 1):
			res.append((self.power(i), i))
		res.sort()
		return res[k - 1][1]

	@lru_cache
	def power(self, num):
		if num == 1:
			return 0
		if num % 2 == 0:
			return 1 + self.power(num // 2)
		else:
			return 1 + self.power(3 * num + 1)


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = {}
		for i in range(lo, hi + 1):
			c = 0
			t = i
			while i != 1:
				if i % 2 == 0:
					i = i // 2
					c += 1
				else:
					i = 3 * i + 1
					c += 1
			d[t] = c
		f = sorted(list(d.items()), key=lambda kv: kv[1])
		return f[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def helper(x):
			steps = 0
			while x != 1:
				if x & 1:
					x = x * 3 + 1
				else:
					x //= 2
				steps += 1
			return steps
		lookup = {}
		for x in range(lo, hi + 1):
			lookup[x] = helper(x)
		ans = sorted(lookup.items(), key=lambda x: x[1])
		return ans[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		res = []
		for num in range(lo, hi + 1):
			steps = 0
			tmp = num
			while num > 1:
				if num % 2:
					num = 3 * num + 1
				else:
					num //= 2
				steps += 1
			res.append((steps, tmp))
		res.sort()
		return res[k - 1][1]


from functools import lru_cache

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		@lru_cache
		def helper(x):
			steps = 0
			while x != 1:
				if x & 1:
					x = x * 3 + 1
				else:
					x //= 2
				steps += 1
			return steps
		lookup = {}
		for x in range(lo, hi + 1):
			lookup[x] = helper(x)
		return sorted(lookup.items(), key=lambda x: x[1])[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		count = 0
		answers = []
		numbers = []
		memo = {}
		for number in range(lo, hi + 1):
			original = number
			numbers.append(numbers)
			count = 0
			while number != 1:
				if number % 2 == 0:
					number = number // 2
					count = count + 1
				else:
					number = 3 * number + 1
					count = count + 1
			memo[original] = count
		sort_memo = sorted(list(memo.items()), key=lambda x: x[1], reverse=False)
		return sort_memo[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = {}
		for i in range(lo, hi + 1):
			self.pow(i, i, d, 0)
		d1 = OrderedDict(sorted(list(d.items()), key=lambda x: x[1]))
		l = list(d1.keys())
		return l[k - 1]

	def pow(self, n1, n, d, c):
		if n == 1:
			d[n1] = c
			return
		if n % 2 == 0:
			n = n / 2
		elif n % 2 == 1:
			n = n * 3 + 1
		c += 1
		if n in d:
			d[n1] = c + d[n]
			return
		self.pow(n1, n, d, c)


class Solution:

	def power(self, number: int):
		count = 0
		while number > 1:
			if number % 2:
				number = 3 * number + 1
			else:
				number //= 2
			count += 1
		return count

	def getKth(self, lo: int, hi: int, k: int) -> int:
		numbers_power = sorted([(self.power(number), number) for number in range(lo, hi + 1)])
		return numbers_power[k - 1][1]


class Solution:

	def get_power(self, n):
		num = 0
		while n != 1:
			if n % 2 == 0:
				n //= 2
			else:
				n = 3 * n + 1
			num += 1
		return num

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power = {}
		for i in range(lo, hi + 1):
			power[i] = self.get_power(i)
		return sorted(list(power.keys()), key=lambda x: power[x])[k - 1]


cache = {1: 0}

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def get_power(x, count=0):
			if x in cache:
				return cache[x] + count
			return get_power(x * 3 + 1 if x & 1 else x // 2, count + 1)
		cache.update({i: get_power(i) for i in range(lo, hi + 1) if i not in cache})
		return sorted((x for x in list(cache.items()) if lo <= x[0] <= hi), key=lambda x: x[1])[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		res = {}
		if lo == 1 and hi == 1 and (k == 1):
			return 1

		def count_steps(x):
			cnt = 0
			if x == 1:
				return cnt
			while x > 1:
				if x % 2 == 0:
					x = x // 2
				else:
					x = x * 3 + 1
				cnt += 1
			return cnt
		for i in range(lo, hi + 1):
			res[i] = count_steps(i)
		return sorted(list(res.items()), key=lambda x: x[1])[k - 1][0]


def power_value(x):
	pv = 0
	while x != 1:
		if x % 2 == 0:
			x = x // 2
		else:
			x = 3 * x + 1
		pv += 1
	return pv

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power_values = []
		for x in range(lo, hi + 1):
			pv_x = power_value(x)
			power_values.append((x, pv_x))
		return sorted(power_values, key=lambda e: e[1])[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def power(n):
			counter = 0
			while n != 1:
				counter += 1
				if n % 2 == 0:
					n = n // 2
				else:
					n = 3 * n + 1
			return counter
		key = [x for x in range(lo, hi + 1)]
		value = [power(x) for x in key]
		ans = list(zip(key, value))
		sorted_ans = sorted(ans, key=lambda t: t[1])
		return sorted_ans[k - 1][0]


from collections import defaultdict

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		po = dict()
		for i in range(lo, hi + 1):
			temp = 0
			curr = i
			while curr != 1:
				if curr & 1:
					child = curr * 3 + 1
				else:
					child = curr // 2
				curr = child
				temp += 1
			po[i] = temp
		res = sorted(po.items(), key=lambda x: x[1])
		return res[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		dict = defaultdict()
		for i in range(lo, hi + 1):
			steps = 0
			j = i
			while i != 1:
				if i % 2 == 0:
					i = i // 2
				else:
					i = 3 * i + 1
				steps += 1
			dict[j] = steps
		dict = sorted(dict.items(), key=lambda x: x[1])
		return dict[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def fun(n):
			if n == 1:
				return 0
			ans = 0
			while n > 1:
				if n % 2 == 0:
					n //= 2
				else:
					n = n * 3 + 1
				ans += 1
			ans += 1
			return ans
		ans = []
		for i in range(lo, hi + 1):
			ans.append([i, fun(i)])
		ans.sort(key=lambda x: x[1])
		for i in range(k):
			if i == k - 1:
				return ans[i][0]


class Solution:
	power = {}

	def get_power(self, num):
		if num == 1:
			return 0
		if num in self.power:
			return self.power[num]
		if num % 2 == 0:
			self.power[num] = self.get_power(num // 2) + 1
		else:
			self.power[num] = self.get_power(3 * num + 1) + 1
		return self.power[num]

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power_vals = {val: self.get_power(val) for val in range(lo, hi + 1)}
		vals = [k for (k, v) in sorted(power_vals.items(), key=lambda x: (x[1], x[0]))]
		return vals[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		lst = []

		def power(s) -> int:
			count = 0
			while s != 1:
				if s % 2 == 0:
					s = s // 2
					count = count + 1
				else:
					s = 3 * s + 1
					count = count + 1
			return (count, s)
		for i in range(lo, hi + 1):
			lst.append((i, power(i)))
		lst.sort(key=lambda x: x[1])
		return lst[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def power(x):
			r = 0
			while x > 1:
				if x % 2 == 0:
					x >>= 1
				else:
					x = 3 * x + 1
				r += 1
			return r
		array = (i for i in range(lo, hi + 1))
		array = sorted(array, key=lambda x: power(x))
		return array[k - 1]


class Solution:

	def calc(self, num):
		count = 0
		while num != 1:
			if num % 2 == 0:
				num = num // 2
			else:
				num = 3 * num + 1
			count += 1
		return count

	def getKth(self, lo: int, hi: int, k: int) -> int:
		counts = []
		keys = [i for i in range(lo, hi + 1)]
		dict = {}
		for i in range(lo, hi + 1):
			ans = self.calc(i)
			counts.append(ans)
		for key in keys:
			for count in counts:
				dict[key] = count
				counts.remove(count)
				break
		dict = {k: v for (k, v) in sorted(list(dict.items()), key=lambda item: item[1])}
		final = [key for key in list(dict.keys())]
		return final[k - 1]


class Solution:

	def getKth(self, lo, hi, k):
		dic = {}
		for n in range(lo, hi + 1):
			steps = self.countStep(n)
			dic[n] = steps
		return sorted(dic.items(), key=lambda x: (x[1], x[0]))[k - 1][0]

	def countStep(self, m):
		step = 0
		while m != 1:
			if m % 2 == 0:
				m //= 2
			else:
				m = m * 3 + 1
			step += 1
		return step


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		arr = []
		for i in range(lo, hi + 1):
			counter = 0
			num = i
			while num != 1:
				if num % 2 == 1:
					num = 3 * num + 1
				else:
					num = num // 2
				counter += 1
			arr.append([i, counter])
		arr.sort()
		for i in arr:
			(i[0], i[1]) = (i[1], i[0])
		arr.sort()
		return arr[k - 1][1]


import heapq

class Solution:

	def calculateSteps(self, num):
		count = 0
		while num > 1:
			if num % 2 == 0:
				num = num // 2
			else:
				num = 3 * num + 1
			count += 1
		return count

	def getKth(self, lo: int, hi: int, k: int) -> int:
		vals = []
		for num in range(lo, hi + 1):
			heapq.heappush(vals, (self.calculateSteps(num), num))
		print(vals)
		count = 1
		val = None
		while count < k:
			heapq.heappop(vals)
			count += 1
		return heapq.heappop(vals)[1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		res = []
		for i in range(lo, hi + 1):
			sol = [i]
			count = 0
			while i != 1:
				if i % 2 == 0:
					i //= 2
				else:
					i = 3 * i + 1
				count += 1
			sol = [count, sol[0]]
			res.append(sol)
		result = sorted(res)
		ff = [x[1] for x in result]
		return ff[k - 1]


class Solution:

	def get_power(self, n):
		res = 0
		while n != 1:
			if n % 2 == 0:
				n //= 2
			else:
				n = 3 * n + 1
			res += 1
		return res

	def getKth(self, lo: int, hi: int, k: int) -> int:
		array = []
		for i in range(lo, hi + 1):
			array.append((i, self.get_power(i)))
		array.sort(key=lambda x: (x[1], x[0]))
		return array[k - 1][0]


class Solution:

	@staticmethod
	def compute_power(x, d={}):
		if x in d:
			return d[x]
		(xcopy, steps) = (x, 0)
		while x != 1 and x not in d:
			x = 3 * x + 1 if x % 2 else x // 2
			steps += 1 + d[x] if x in d else 1
		d[xcopy] = steps
		return steps

	def getKth(self, lo, hi, k):
		vals = list(range(lo, hi + 1))
		vals.sort(key=lambda x: self.compute_power(x))
		return vals[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		ans = {}
		for i in range(lo, hi + 1):
			j = i
			s = 0
			while i != 1:
				if i % 2 == 0:
					i = i // 2
				else:
					i = i * 3 + 1
				s = s + 1
			ans[j] = s
		ans = sorted(list(ans.items()), key=lambda x: x[1])
		return ans[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def getPower(x):
			count = 0
			while x != 1:
				if x % 2 == 0:
					x = x // 2
				else:
					x = 3 * x + 1
				count += 1
			return count
		output = [[getPower(x), x] for x in range(lo, hi + 1)]
		output.sort(key=lambda x: (x[0], x[1]))
		return output[k - 1][1]


class Solution:

	def __init__(self):
		self.cache = {1: 0, 2: 1, 3: 7, 4: 2}

	def getPower(self, n):
		after = 0
		steps = 0
		if n % 4 == 0:
			after = n // 4
			steps = 2
		elif n % 4 == 1:
			after = n // 4 * 3 + 1
			steps = 3
		elif n % 4 == 2:
			after = n // 4 * 3 + 2
			steps = 3
		else:
			after = n // 4 * 9 + 8
			steps = 4
		if after in list(self.cache.keys()):
			return self.cache[after] + steps
		else:
			return self.getPower(after) + steps

	def getKth(self, low, high, k):
		data = [self.getPower(i) for i in range(low, high + 1)]
		sorted_data = sorted(zip(data, list(range(len(data)))), key=lambda x: x[0])
		return sorted_data[k - 1][1] + low


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		heap = []
		for i in range(lo, hi + 1):
			ret = i
			steps = 0
			while ret != 1:
				if ret % 2 == 0:
					ret = ret // 2
				else:
					ret = 3 * ret + 1
				steps += 1
			heapq.heappush(heap, (-steps, -i))
			if len(heap) > k:
				heapq.heappop(heap)
		return -heap[0][1]


class Solution:

	def findPower(self, ele):
		ctr = 0
		while ele != 1:
			if ele % 2 == 0:
				ele = ele // 2
			else:
				ele = 3 * ele + 1
			ctr += 1
		return ctr

	def getKth(self, lo: int, hi: int, k: int) -> int:
		powmat = []
		for i in range(lo, hi + 1):
			ct = self.findPower(i)
			powmat.append([ct, i])
		powmat.sort()
		print(powmat)
		return powmat[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		arr = []
		for i in range(lo, hi + 1):
			arr.append([self.getPower(i), i])
		arr.sort(key=lambda x: (x[0], x[1]))
		return arr[k - 1][1]

	def getPower(self, number: int) -> int:
		count = 0
		while number != 1:
			if number % 2 == 1:
				number = 3 * number + 1
			else:
				number //= 2
			count += 1
		return count


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def power(x):
			count = 0
			while x > 1:
				if x % 2:
					x = 3 * x + 1
				else:
					x = x / 2
				count += 1
			return count
		return sorted(range(lo, hi + 1), key=power)[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		res = []
		for i in range(lo, hi + 1):
			count = 0
			j = i
			while j > 1:
				if j & 1:
					j = 3 * j + 1
				else:
					j //= 2
				count += 1
			res.append((count, i))
		res.sort()
		return res[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		arr = []

		def power(x):
			count = 0
			while x != 1:
				if x % 2 == 0:
					x = x // 2
					count += 1
				elif x % 2 != 0:
					x = 3 * x + 1
					count += 1
			return count
		for i in range(lo, hi + 1):
			p = power(i)
			arr.append((i, p))
		arr = [j[0] for j in sorted(arr, key=lambda x: x[1])]
		return arr[k - 1]


class Solution:
	dp = {}

	def findPower(self, num):
		way = [num]
		ops = 0
		while num != 1 and num not in self.dp:
			if num % 2 == 0:
				num /= 2
			else:
				num = num * 3 + 1
			way.append(num)
			ops += 1
		if num in self.dp:
			ops += self.dp[num]
		for prev in way:
			self.dp[prev] = ops
			ops -= 1

	def getKth(self, lo: int, hi: int, k: int) -> int:
		res = []
		for i in range(lo, hi + 1):
			self.findPower(i)
			res.append((i, self.dp[i]))
		res = sorted(res, key=lambda x: x[1])
		return res[k - 1][0]


from operator import itemgetter

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		z = []
		for i in range(lo, hi + 1):
			count = 0
			f = i
			while i != 1:
				if i % 2 == 0:
					i = i / 2
					count += 1
				else:
					i = 3 * i + 1
					count += 1
			z.append([f, count])
		return sorted(z, key=itemgetter(1))[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		res = []
		dict1 = {}
		for i in range(lo, hi + 1, 1):
			c = 0
			r = []
			v = 0
			p = i
			while c == 0:
				if i == 1:
					c = 1
				elif i % 2 == 0:
					i = i // 2
					v += 1
					while i % 2 == 0:
						i = i // 2
						v += 1
				else:
					i = i * 3 + 1
					v += 1
			r.append(p)
			r.append(v)
			res.append(r)
		res.sort(key=lambda x: x[1])
		print(res)
		return res[k - 1][0]


class Solution:

	def power_value(self, n):
		count = 0
		while n != 1:
			count += 1
			if n % 2 == 0:
				n /= 2
			else:
				n = n * 3 + 1
		return count

	def getKth(self, lo: int, hi: int, k: int) -> int:
		vals = sorted(list(range(lo, hi + 1)), key=self.power_value)
		return vals[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		dic = {}

		def determine_power(a):
			power = 0
			while a > 1:
				if a % 2:
					a = 3 * a + 1
					power += 1
				else:
					a = a / 2
					power += 1
			return power
		for element in range(lo, hi + 1):
			p = determine_power(element)
			dic.update({element: p})
		dd = sorted(list(dic.items()), key=lambda x: x[1])
		return dd[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		ans = {}
		for num in range(lo, hi + 1):
			num_copy = num
			steps = 0
			while num_copy != 1:
				if num_copy % 2 == 0:
					num_copy = num_copy / 2
					steps += 1
				else:
					num_copy = 3 * num_copy + 1
					steps += 1
			ans[num] = steps
		return sorted(list(ans.items()), key=lambda item: item[1])[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def powerx(x):
			p = 0
			while x != 1:
				if x % 2 == 0:
					x = x / 2
				else:
					x = x * 3 + 1
				p += 1
			return p
		dic = {}
		for i in range(lo, hi + 1):
			dic[i] = powerx(i)
		dic_ordered = sorted(list(dic.items()), key=lambda x: x[1])
		return dic_ordered[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def getPower(x):
			count = 0
			while x != 1:
				if x % 2 == 0:
					x /= 2
					count += 1
				else:
					x = 3 * x + 1
					count += 1
			return count
		dic = {}
		for i in range(lo, hi + 1):
			dic[i] = getPower(i)
		sorted_dic = sorted(list(dic.items()), key=lambda x: x[1], reverse=False)
		print(sorted_dic)
		for i in range(len(sorted_dic)):
			if i == k - 1:
				return sorted_dic[i][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def getPowerValue(num):
			num_steps = 0
			while num != 1:
				if num % 2 == 0:
					num = num / 2
				else:
					num = 3 * num + 1
				num_steps += 1
			return num_steps
		powervalues = sorted([i for i in range(lo, hi + 1)], key=getPowerValue)
		return powervalues[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power_values = defaultdict()
		for i in range(lo, hi + 1):
			count = 0
			x = i
			while x != 1:
				if x % 2 == 0:
					x /= 2
				else:
					x = 3 * x + 1
				count += 1
			power_values[i] = count
		sorted_d = sorted(power_values.items(), key=lambda x: x[1])
		return sorted_d[k - 1][0]


class Solution:
	powers = {1: 0}

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power_range = []
		for i in range(lo, hi + 1):
			tup = (i, self.getPower(i))
			power_range.append(tup)
		power_range.sort(key=lambda x: x[1])
		return power_range[k - 1][0]

	def getPower(self, num):
		if num in self.powers:
			return self.powers[num]
		if num % 2 == 1:
			power = self.getPower(num * 3 + 1) + 1
			self.powers[num] = power
			return power
		else:
			power = self.getPower(num / 2) + 1
			self.powers[num] = power
			return power


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def getPower(num):
			if num == 1:
				return 1
			count = 0
			while num != 1:
				if num % 2 == 0:
					num = num / 2
					count += 1
				else:
					num = 3 * num + 1
					count += 1
			return count
		dic = {}
		for i in range(lo, hi + 1):
			dic[i] = getPower(i)
		dic = {k: v for (k, v) in sorted(dic.items())}
		dic = {k: v for (k, v) in sorted(list(dic.items()), key=lambda item: item[1])}
		return list(dic.keys())[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		return sorted(map(lambda x: (self.myfunc(x), x), range(lo, hi + 1)))[k - 1][1]

	def myfunc(self, x):
		transformations = 0
		while x != 1:
			if x % 2 == 0:
				x = x / 2
			else:
				x = 3 * x + 1
			transformations += 1
		return transformations


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		indexList = [i for i in range(lo, hi + 1, 1)]
		powerList = [self.getPower(i) for i in indexList]
		sortedIndex = [x for (_, x) in sorted(zip(powerList, indexList))]
		return sortedIndex[k - 1]

	def getPower(self, x: int) -> int:
		count = 0
		while x != 1:
			if x % 2 == 0:
				x = x / 2
			else:
				x = 3 * x + 1
			count += 1
		return count


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		low = lo
		high = hi
		countlist = []
		intgererlist = []
		for lo in range(low, high + 1):
			i = lo
			count = 0
			while lo > 1:
				if lo % 2 == 0:
					lo = lo // 2
				else:
					lo = 3 * lo + 1
				count += 1
			countlist.append(count)
			intgererlist.append(i)
		ziped = zip(countlist, intgererlist)
		o = 0
		for (i, j) in sorted(ziped):
			o += 1
			if o == k:
				return j


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		powerSteps = []
		for i in range(lo, hi + 1):
			powerSteps.append((self.getPowerSteps(i), i))
		powerSteps.sort()
		return powerSteps[k - 1][1]

	def getPowerSteps(self, value):
		steps = 0
		while value != 1:
			if value % 2 == 0:
				value = value / 2
			else:
				value = 3 * value + 1
			steps += 1
		return steps


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = dict()
		for i in range(lo, hi + 1):
			res = 0
			x = i
			while i != 1:
				if i % 2 == 1:
					i = 3 * i + 1
				else:
					i = i / 2
				res += 1
			d[x] = res
		di = {k: v for (k, v) in sorted(d.items(), key=lambda item: item[1])}
		return list(di.keys())[k - 1]


class Solution:

	def getKth(self, lo, hi, k):

		def power(x):
			if x & 1:
				return 0 if x == 1 else 1 + power(3 * x + 1)
			return 1 + power(x >> 1)
		A = [(power(x), x) for x in range(lo, hi + 1)]
		return sorted(A)[k - 1][1]


def fun(x):
	cnt = 0
	while x != 1:
		x = x / 2 if x % 2 == 0 else 3 * x + 1
		cnt += 1
	return cnt

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		lst = sorted([(x, fun(x)) for x in range(lo, hi + 1)], key=lambda x: (x[1], x[0]))
		print(lst, k)
		return lst[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		dic = {}
		for x in range(lo, hi + 1):
			dic[x] = self.get_power(x, 0)
		dic_2 = {k: dic[k] for k in sorted(dic, key=dic.get)}
		return list(dic_2.keys())[k - 1]

	def get_power(self, x: int, p: int) -> int:
		while x != 1:
			if x % 2 == 0:
				x //= 2
			else:
				x = 3 * x + 1
			p += 1
		return p


@lru_cache(maxsize=1000)
def pow(n: int):
	if n == 1:
		return 1
	if n % 2 == 0:
		return 1 + pow(n // 2)
	else:
		return 1 + pow(3 * n + 1)

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		l = list(range(lo, hi + 1))
		l.sort(key=lambda x: (pow(x), x))
		return l[k - 1]


class Solution:

	def getSteps(self, x):
		res = 0
		while x != 1:
			if x % 2 == 1:
				x = 3 * x + 1
			else:
				x = x / 2
			res += 1
		return res

	def getKth(self, lo: int, hi: int, k: int) -> int:
		res = []
		for i in range(lo, hi + 1, 1):
			val = self.getSteps(i)
			res.append([i, val])
		print(res)
		res.sort(key=lambda x: (x[1], x[0]))
		ans = [item[0] for item in res]
		print(ans)
		return ans[k - 1]


import functools

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		arr = []
		for i in range(lo, hi + 1):
			arr.append([i, getPower(i)])
		arr.sort(key=functools.cmp_to_key(compareByK))
		return arr[k - 1][0]

def getPower(n):
	steps = 0
	while n != 1:
		steps += 1
		if n % 2 == 0:
			n = n / 2
		else:
			n = n * 3 + 1
	return steps

def compareByK(x, y):
	powerX = x[1]
	powerY = y[1]
	if powerX < powerY:
		return -1
	elif powerX > powerY:
		return 1
	elif x[0] < y[0]:
		return -1
	elif x[0] > y[0]:
		return 1
	else:
		return 0


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		int_to_steps = {}
		for x in range(lo, hi + 1):
			start = x
			steps = 0
			while x != 1:
				steps += 1
				if x % 2 == 0:
					x = x / 2
				else:
					x = x * 3 + 1
			int_to_steps[start] = steps
		return sorted(list(int_to_steps.items()), key=lambda item: item[1])[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		nums = list(range(lo, hi + 1))
		count = 0
		while True:
			for i in range(len(nums)):
				if nums[i] == 0:
					continue
				elif nums[i] == 1:
					count += 1
					nums[i] = 0
					if count == k:
						return lo + i
				elif nums[i] % 2 == 0:
					nums[i] = nums[i] // 2
				else:
					nums[i] = 3 * nums[i] + 1
				if nums[i] == 1:
					count += 1
					nums[i] = 0
					if count == k:
						return lo + i


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		if lo == hi:
			return lo
		ans = []
		for i in range(lo, hi + 1):
			num = i
			ctr = 0
			while num != 1:
				if num % 2 != 0:
					num = num * 3 + 1
				else:
					num = num / 2
				ctr += 1
			ans.append((ctr, i))
		return sorted(ans, key=lambda x: x[0])[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def power(n: int):
			step = 0
			while n != 1:
				step += 1
				if n % 2 == 0:
					n = n / 2
				else:
					n = n * 3 + 1
			return step
		nums = list(range(lo, hi + 1))
		powers = [power(n) for n in nums]
		sortedIndex = list(range(0, hi - lo + 1))
		sortedIndex = sorted(sortedIndex, key=lambda x: (powers[x], nums[x]))
		return sortedIndex[k - 1] + lo


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		powers = {}
		l = []
		for i in range(lo, hi + 1):
			j = i
			stack = []
			stack.append(j)
			if j not in powers:
				while j != 1:
					if j % 2 == 0:
						j = j // 2
						stack.append(j)
					else:
						j = j * 3 + 1
						stack.append(j)
				cnt = 0
				while stack:
					j = stack.pop()
					powers[j] = cnt
					cnt += 1
			l.append((i, powers[i]))
		l = sorted(l, key=lambda x: (x[1], x[0]))
		return l[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def power(n: int) -> int:
			step = 0
			while n > 1:
				step += 1
				if n % 2 == 0:
					n = n / 2
				else:
					n = 3 * n + 1
			return step
		interval = [i for i in range(lo, hi + 1)]
		pwr = [[j, power(j)] for j in range(lo, hi + 1)]
		pwr = sorted(pwr, key=lambda x: x[1])
		return pwr[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		arr_of_powers = {}

		def get_int_power(num):
			pwr = 0
			temp = num
			while temp != 1:
				pwr += 1
				if temp % 2 == 0:
					temp /= 2
				elif temp % 2 == 1:
					temp = 3 * temp + 1
			return pwr
		for num in range(lo, hi + 1):
			arr_of_powers[num] = get_int_power(num)
		interval = sorted(arr_of_powers.items(), key=lambda x: x[1])
		return interval[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		@lru_cache(None)
		def power(x):
			if x == 1:
				return 0
			if x % 2 == 0:
				return 1 + power(x // 2)
			return 1 + power(3 * x + 1)
		return sorted(range(lo, hi + 1), key=power)[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def getSteps(lo):
			steps = 0
			reduced = lo
			while reduced != 1:
				if reduced % 2 == 0:
					reduced = reduced / 2
				else:
					reduced = 3 * reduced + 1
				steps += 1
			return steps
		a = {}
		for i in range(lo, hi + 1):
			steps = getSteps(i)
			if steps not in a:
				a[steps] = [i]
			else:
				a[steps].append(i)
		r = []
		for key in sorted(a.keys()):
			for val in a[key]:
				r.append(val)
		return r[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def getF(x):
			if x == 1:
				return 0
			return getF(3 * x + 1) + 1 if x % 2 == 1 else getF(x // 2) + 1
		weights = list(range(lo, hi + 1))
		weights = sorted(weights, key=lambda x: getF(x))
		return weights[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		powers = []
		for i in range(lo, hi + 1):
			index = i
			steps = 0
			while i != 1:
				if i % 2 == 0:
					i = i / 2
					steps += 1
				else:
					i = 3 * i + 1
					steps += 1
			powers.append([steps, index])
		sortPowers = sorted(powers)
		return sortPowers[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def power(num):
			res = 0
			while num != 1:
				if num % 2 == 0:
					num = num / 2
				else:
					num = 3 * num + 1
				res += 1
			return res
		heap = []
		for i in range(lo, hi + 1):
			heap.append((power(i), i))
		heapq.heapify(heap)
		for i in range(k - 1):
			heapq.heappop(heap)
		return heap[0][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		dic = {}
		for i in range(lo, hi + 1):
			power = self.findPower(i, 0)
			dic[i] = power
		sortedValue = sorted(dic.items(), key=lambda x: x[1])
		return sortedValue[k - 1][0]

	def findPower(self, num, count):
		if num == 1:
			return count
		elif num % 2 == 0:
			return self.findPower(num // 2, count + 1)
		else:
			return self.findPower(3 * num + 1, count + 1)


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def transform(v):
			times = 0
			while v != 1:
				times += 1
				if v % 2 == 0:
					v = v / 2
				else:
					v = 3 * v + 1
			return times
		res = []
		for x in range(lo, hi + 1):
			power = transform(x)
			res.append([power, x])
		res.sort(key=lambda x: (x[0], x[1]))
		return res[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		pair = []

		def transform(val):
			count = 0
			while val != 1:
				val = val / 2 if val % 2 == 0 else 3 * val + 1
				count += 1
			return count
		for i in range(lo, hi + 1):
			pair.append((transform(i), i))
		print(sorted(pair))
		return sorted(pair)[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def power(x):
			if x == 1:
				return 0
			if x % 2 == 0:
				return 1 + power(x // 2)
			return 1 + power(3 * x + 1)
		return sorted(range(lo, hi + 1), key=power)[k - 1]
		len_powers = [0] * (hi - lo + 1)
		for n in range(lo, hi + 1):
			ls_power = [n]
			while ls_power[-1] != 1:
				if ls_power[-1] % 2 == 0:
					ls_power.append(ls_power[-1] // 2)
				else:
					ls_power.append(3 * ls_power[-1] + 1)
			len_powers[n - lo] = len(ls_power) - 1
		return sorted(zip(range(lo, hi + 1), len_powers), key=lambda x: [x[1], x[0]])[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		nums = [i for i in range(lo, hi + 1)]
		powers = [0] * len(nums)
		for i in range(len(nums)):
			cur = nums[i]
			while cur != 1:
				if cur % 2 == 0:
					cur = cur / 2
				else:
					cur = 3 * cur + 1
				powers[i] += 1
		result = [x for (_, x) in sorted(zip(powers, nums))]
		return result[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def getPower(n):
			step = 0
			while n != 1:
				n = 3 * n + 1 if n % 2 else n / 2
				step += 1
			return step
		powers = sorted([(i, getPower(i)) for i in range(lo, hi + 1)], key=lambda x: (x[1], x[0]))
		return powers[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def getPow(n):
			c = 0
			while n != 1:
				if n % 2 == 0:
					n //= 2
				else:
					n = 3 * n + 1
				c += 1
			return c

		def func():
			arr = {i: getPow(i) for i in range(lo, hi + 1)}
			v = list(set(arr.values()))
			v.sort()
			fin = []
			for i in v:
				t = []
				for (a, b) in arr.items():
					if b == i:
						t.append(a)
				t.sort()
				fin.extend(t)
			return fin[k - 1]
		return func()


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		heap = []
		for i in range(lo, hi + 1):
			power = self.computer_power(i)
			heapq.heappush(heap, (power, i))
		k_now = 1
		while heap:
			(new_power, i) = heapq.heappop(heap)
			if k_now == k:
				return i
			k_now += 1
		return result

	def computer_power(self, val):
		if val == 1:
			return 0
		if val % 2 == 0:
			return 1 + self.computer_power(val // 2)
		else:
			return 1 + self.computer_power(3 * val + 1)


class Solution:

	def get_power(self, n):
		if n == 1:
			return 0
		elif n % 2 == 0:
			return 1 + self.get_power(n // 2)
		else:
			return 1 + self.get_power(3 * n + 1)

	def getKth(self, lo: int, hi: int, k: int) -> int:
		nums = [i for i in range(lo, hi + 1)]
		lst2 = []
		for num in nums:
			lst2.append((num, self.get_power(num)))
		lst2.sort(key=lambda x: x[1])
		return lst2[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		res = []

		def power(num):
			if num == 2:
				return 1
			elif num % 2 == 0:
				return 1 + power(num // 2)
			else:
				return 1 + power(3 * num + 1)
		dic = collections.defaultdict(list)
		for i in range(lo, hi + 1):
			dic[power(i)].append(i)
		for (_, v) in sorted(dic.items()):
			res += v
		return res[k - 1]


class Solution:

	def __init__(self):
		self.memo = {}

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power = [0 for i in range(lo, hi + 1)]
		for i in range(lo, hi + 1):
			if i in self.memo:
				power[i - lo] = self.memo[i]
			else:
				power[i - lo] = (self.get_power(i, 0), i)
				self.memo[i] = power[i - lo]
		power.sort()
		return power[k - 1][1]

	def get_power(self, i, curr_pow):
		if i == 1:
			return curr_pow
		if i % 2 == 0:
			return self.get_power(i / 2, curr_pow + 1)
		else:
			return self.get_power((i - 1) / 2 * 3 + 2, curr_pow + 2)


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def helper(num):
			if num == 1:
				return 0
			if num % 2 == 0:
				return helper(num // 2) + 1
			else:
				return helper(num * 3 + 1) + 1
		res = []
		for i in range(lo, hi + 1):
			res.append((helper(i), i))
		res.sort()
		return res[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		return sorted(((get_power_value(x), x) for x in range(lo, hi + 1)))[k - 1][1]

def get_power_value(x):
	if x == 1:
		return 0
	return 1 + get_power_value(x / 2 if x % 2 == 0 else x * 3 + 1)


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def transform(x):
			steps = 0
			while x != 1:
				if x & 1 == 0:
					x //= 2
				else:
					x = 3 * x + 1
				steps += 1
			return steps
		arr = list(range(lo, hi + 1))
		arr.sort(key=lambda x: (transform(x), x))
		return arr[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		cache = [0] * 999999
		for num in range(lo, hi + 1):
			if cache[num] != 0:
				continue
			path = [num]
			while num != 1 and cache[num] == 0:
				if num % 2 == 0:
					num //= 2
					path.append(num)
				else:
					num = num * 3 + 1
					path.append(num)
			for (idx, n) in enumerate(path):
				if cache[n] != 0:
					break
				cache[n] = len(path) - 1 - idx + cache[path[-1]]
		res = [(i + lo, steps) for (i, steps) in enumerate(cache[lo:hi + 1])]
		res = sorted(res, key=lambda _: _[1])
		return res[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def find_power_value(n: int, steps: int) -> int:
			if n == 2:
				return steps + 1
			if n % 2 == 0:
				return find_power_value(n // 2, steps + 1)
			return find_power_value(3 * n + 1, steps + 1)
		result = []
		for i in range(lo, hi + 1):
			result.append((find_power_value(i, 0), i))
		result.sort()
		return result[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		memo = {1: 0}

		def power(x):
			if x in memo:
				return memo[x]
			n = memo[x] = 1 + power(3 * x + 1 if x & 1 else x >> 1)
			return n
		ans = [(x, power(x)) for x in range(lo, hi + 1)]
		sorted_ans = sorted(ans, key=lambda t: t[1])
		return sorted_ans[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def process(x, nsteps):
			if x == 2:
				return nsteps
			elif x % 2 == 0:
				return process(x // 2, nsteps + 1)
			else:
				return process(x * 3 + 1, nsteps + 1)
		sol = []
		for i in range(lo, hi + 1):
			sol.append((process(i, 0), i))
		sol.sort()
		return sol[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		g = {}
		for i in range(lo, hi + 1):
			p = self.power(i, 0)
			g[i] = p
		s = sorted(list(g.items()), key=lambda x: x[1])
		return s[k - 1][0]

	def power(self, num, count):
		if num == 1:
			return count
		elif num % 2 == 0:
			return self.power(num // 2, count + 1)
		else:
			return self.power(3 * num + 1, count + 1)


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		x = {}
		for i in range(lo, hi + 1):
			j = []
			g = i
			while i != 1:
				if i % 2 == 0:
					i = i / 2
					j.append(i)
				else:
					i = 3 * i + 1
					j.append(i)
			x[g] = len(j)
		x = sorted(x, key=x.get)
		return x[k - 1]


class Solution:

	def transform(self, num, count=0):
		if num == 1:
			return count
		elif num % 2 == 0:
			return self.transform(num // 2, count + 1)
		else:
			return self.transform(num * 3 + 1, count + 1)

	def getKth(self, lo: int, hi: int, k: int) -> int:
		p_list = []
		for i in range(lo, hi + 1):
			p_list.append((self.transform(i), i))
		p_list.sort()
		return p_list[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def getPower(num: int) -> int:
			if num == 1:
				return 0
			if num % 2 == 0:
				return 1 + getPower(num // 2)
			if num % 2 == 1:
				return 1 + getPower(3 * num + 1)
		powers = []
		for cand in range(lo, hi + 1):
			powers.append((cand, getPower(cand)))
		powers = sorted(powers, key=lambda x: x[1])
		return powers[k - 1][0]


import heapq

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def power(num, cou=0):
			if num == 1:
				return cou
			if num % 2 == 0:
				num = num // 2
				return power(num, cou + 1)
			else:
				num = 3 * num + 1
				return power(num, cou + 1)
		arr = []
		while lo <= hi:
			j = power(lo)
			heapq.heappush(arr, (-j, -lo))
			if len(arr) > k:
				heapq.heappop(arr)
			lo += 1
		return -heapq.heappop(arr)[1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def key_func(val):

			def recur(val):
				if val <= 1:
					return 0
				if val % 2 == 0:
					return recur(val / 2) + 1
				return recur(val * 3 + 1) + 1
			return recur(val)
		out = [i for i in range(lo, hi + 1)]
		out.sort(key=key_func)
		return out[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		output = {}
		for i in range(lo, hi + 1):
			a = i
			counter = 0
			while i > 1:
				if i % 2 == 0:
					i = i / 2
				else:
					i = 3 * i + 1
				counter += 1
			output[a] = counter
		output = sorted(output.items(), key=lambda x: x[1])
		return output[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = {}

		def helper(i):
			if i == 1:
				return 0
			if i in d:
				return d[i]
			if i % 2 == 0:
				return 1 + helper(i // 2)
			else:
				return 1 + helper(3 * i + 1)
		ans = [[helper(i), i] for i in range(lo, hi + 1)]
		ans.sort()
		return ans[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		st = [0] * (hi + 1 - lo)
		std = {}
		for x in range(lo, hi + 1):
			i = x
			while x != 1:
				st[i - lo] += 1
				if x % 2 == 0:
					x = x / 2
				else:
					x = 3 * x + 1
			if st[i - lo] in list(std.keys()):
				std[st[i - lo]].append(i)
			else:
				std[st[i - lo]] = [i]
		s_val = sorted(list(std.keys()))
		ans = std[s_val[0]]
		for i in range(1, len(s_val)):
			ans = ans + std[s_val[i]]
		return ans[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def find_transform(x):
			k = [x]
			while k[-1] != 1:
				if x % 2 == 0:
					x = x / 2
					k.append(x)
				else:
					x = x * 3 + 1
					k.append(x)
			return len(k) - 1
		power = []
		for i in range(lo, hi + 1):
			power.append([i, find_transform(i)])
		return sorted(power, key=lambda x: x[1])[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		dp_steps = {}

		def find_power(n: int) -> int:
			if n in dp_steps:
				return dp_steps[n]
			elif n == 1:
				return 0
			elif n % 2 == 0:
				return 1 + find_power(n // 2)
			else:
				return 1 + find_power(n * 3 + 1)
		results = []
		for i in range(lo, hi + 1):
			results.append((find_power(i), i))
		results.sort()
		return results[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		degree_cache = {}

		def find_degree(n, degree=0):
			if n == 1:
				return degree
			if n % 2 == 0:
				degree = find_degree(n // 2, degree + 1)
			else:
				degree = find_degree(n * 3 + 1, degree + 1)
			return degree
		d = {}
		for i in range(lo, hi + 1):
			d[i] = find_degree(i, 0)
		sd = sorted(d.items(), key=lambda x: (x[1], x[0]))
		return sd[k - 1][0]


from collections import defaultdict

def getPower(i):
	if i == 1:
		return 0
	if i % 2 == 0:
		return getPower(i / 2) + 1
	else:
		return getPower(i * 3 + 1) + 1

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = defaultdict(int)
		for i in range(lo, hi + 1):
			d[i] = getPower(i)
		sd = {k: v for (k, v) in sorted(list(d.items()), key=lambda item: item[1])}
		return list(sd)[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power_dic = {}
		powers = []
		for num in range(lo, hi + 1):
			powers.append([self.powerOf(num, 0, power_dic), num])
		return sorted(powers, key=lambda x: x[0])[k - 1][1]

	def powerOf(self, x, steps, power_dic):
		if x == 1:
			return steps
		if x & 1 == 0:
			return self.powerOf(x // 2, steps + 1, power_dic)
		else:
			return self.powerOf(3 * x + 1, steps + 1, power_dic)


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		track = []
		for i in range(lo, hi + 1):
			power = 0
			x = i
			while i != 1:
				if i % 2 == 0:
					i = i // 2
				else:
					i = 3 * i + 1
				power += 1
			track.append([x, power])
		sorted_tr = sorted(track, key=lambda x: [x[1], x[0]])
		print(sorted_tr)
		return sorted_tr[k - 1][0]

	def getPower(self, c, n):
		if int(n) == 1:
			return c
		elif n % 2 == 0:
			self.getPower(c + 1, n / 2)
		else:
			self.getPower(c + 1, 3 * n + 1)


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = {}
		for n in range(lo, hi + 1):
			count = 0
			p = n
			while n != 1:
				if n % 2 == 0:
					n = n / 2
					count = count + 1
				elif n % 2 == 1:
					n = 3 * n + 1
					count = count + 1
			d[p] = count
		return sorted(list(d.items()), key=lambda x: x[1])[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def getPower(n):
			step = 0
			while n != 1:
				if n % 2 == 0:
					n = int(n / 2)
				else:
					n = n * 3 + 1
				step += 1
			return step
		ans = []
		for i in range(lo, hi + 1):
			ip = getPower(i)
			ans.append((ip, i))
		ans.sort()
		return ans[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		nums = []
		for i in range(lo, hi + 1):
			(temp, steps) = (i, 0)
			while temp != 1:
				if temp % 2 == 0:
					temp //= 2
				else:
					temp = 3 * temp + 1
				steps += 1
			nums.append([i, steps])
		nums = sorted(nums, key=lambda n: n[1])
		return nums[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = {}

		def steps(num, level):
			if num == 1:
				return level
			if num % 2 == 0:
				return steps(num / 2, level + 1)
			else:
				return steps(3 * num + 1, level + 1)
		ans = [(steps(x, 0), x) for x in range(lo, hi + 1)]
		ans.sort()
		return ans[k - 1][-1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		a = [i for i in range(lo, hi + 1)]
		z = []

		def cv(s, c):
			if s % 2 == 0:
				s = s / 2
			else:
				s = 3 * s + 1
			c = c + 1
			if s == 1:
				return c
			return cv(s, c)
		for i in a:
			c = 0
			b = cv(i, c)
			z.append([b, i])
		z.sort(key=lambda x: x[0])
		a = []
		for i in z:
			a.append(i[1])
		return a[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		dict = defaultdict()

		def weight(x):
			if x == 1:
				return 1
			if x % 2 == 0:
				return 1 + weight(x // 2)
			else:
				return 1 + weight(3 * x + 1)
		for i in range(lo, hi + 1):
			dict[i] = weight(i)
		dict = sorted(list(dict.items()), key=lambda x: x[1])
		return dict[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def collatz(num, moves=0):
			if num == 1:
				return moves
			if num % 2 == 0:
				return collatz(num / 2, moves + 1)
			else:
				return collatz(num * 3 + 1, moves + 1)
		arr = [(i, collatz(i)) for i in range(lo, hi + 1)]
		arr.sort(key=lambda x: x[1])
		print(arr)
		return arr[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, z: int) -> int:
		d = {}

		def dfs(k):
			if k == 1:
				return
			elif k % 2 == 0:
				c[0] += 1
				dfs(k // 2)
			else:
				c[0] += 1
				dfs(3 * k + 1)
		for i in range(lo, hi + 1):
			c = [0]
			dfs(i)
			d[i] = c[0]
		d = sorted(list(d.items()), key=lambda g: g[1])
		return d[z - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def step(n, i) -> int:
			s = 0
			while n != 1:
				if n % 2 == 0:
					n = n / 2
				else:
					n = n * 3 + 1
				s += 1
			return s
		a = 0
		l = []
		for i in range(lo, hi + 1):
			a = step(i, 0)
			l.append((i, a))
		l = sorted(l, key=lambda x: x[1])
		return l[k - 1][0]


class PowerValue(tuple):

	def __lt__(x, y):
		return x[1] < y[1] if x[1] != y[1] else x[0] < y[0]

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		all_val = [i for i in range(lo, hi + 1)]
		pow_values = []

		def power(val):
			if val == 1:
				return 0
			if val % 2 == 0:
				val = val // 2
			else:
				val = 3 * val + 1
			return 1 + power(val)
		for num in all_val:
			get_pow = power(num)
			pow_values.append((get_pow, num))
		pow_values.sort()
		return pow_values[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def distance(n):
			if n == 1:
				return 0
			new_n = n // 2 if n % 2 == 0 else n * 3 + 1
			return 1 + distance(new_n)
		nums = list(range(lo, hi + 1))
		nums.sort(key=lambda x: (distance(x), x))
		return nums[k - 1]


from functools import cmp_to_key

class Solution:

	def getPower(self, number):
		if number == 1:
			return 0
		if number % 2 == 0:
			return 1 + self.getPower(number / 2)
		else:
			return 1 + self.getPower(number * 3 + 1)

	def getKth(self, lo: int, hi: int, k: int) -> int:
		a = []
		for i in range(lo, hi + 1):
			a.append((i, self.getPower(i)))
		a = sorted(a, key=cmp_to_key(lambda x, y: x[1] - y[1] if x[1] != y[1] else x[0] - y[0]))
		print(a)
		return a[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def get_power_of_element(x):
			if x == 1:
				return 0
			elif x % 2 == 0:
				x = x / 2
				return 1 + get_power_of_element(x)
			elif x % 2 != 0:
				x = 3 * x + 1
				return 1 + get_power_of_element(x)
		array_of_numbers = [x for x in range(lo, hi + 1)]
		array_of_values = []
		for i in array_of_numbers:
			k_value = get_power_of_element(i)
			array_of_values.append((k_value, i))
		array_of_values.sort(key=lambda x: x[0])
		return array_of_values[k - 1][1]


from collections import defaultdict

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = defaultdict(list)
		for integer in range(lo, hi + 1):
			res = integer
			cnt = 0
			while res != 1:
				if res % 2 == 0:
					res /= 2
				elif res % 2 == 1:
					res = res * 3 + 1
				cnt += 1
			d[cnt].append(integer)
		keys = sorted(d.keys())
		ans = []
		for key in keys:
			ans += sorted(d[key])
		return ans[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		track = dict()
		for i in range(lo, hi + 1):
			power = 0
			x = i
			while i != 1:
				if i % 2 == 0:
					i = i // 2
				else:
					i = 3 * i + 1
				power += 1
			track[x] = power
		sorted_tr = sorted(track.items(), key=lambda x: [x[1], x[0]])
		print(sorted_tr)
		return sorted_tr[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		ans = []
		for nn in range(lo, hi + 1):
			ans.append([nn, self.powerVal(nn)])
		ans = sorted(ans, key=lambda x: x[1])
		return ans[k - 1][0]

	def powerVal(self, num):
		count = 0
		while num > 1:
			if num % 2 == 0:
				num = num / 2
			else:
				num = 3 * num + 1
			count += 1
		return count


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		return sorted([(self.recursive(x, 0, {}), x) for x in range(lo, hi + 1)])[k - 1][1]

	def recursive(self, x, count, memo):
		if x in memo:
			return memo[x]
		elif x == 1:
			memo[x] = count
			return count
		elif x % 2 == 0:
			return self.recursive(x / 2, count + 1, memo)
		else:
			return self.recursive(3 * x + 1, count + 1, memo)


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = dict()
		for i in range(lo, hi + 1):
			a = i
			c = 0
			while a > 1:
				if a % 2 == 0:
					a = a / 2
					c += 1
				else:
					a = 3 * a + 1
					c += 1
			d[i] = c
		res = sorted(list(d.items()), key=lambda x: x[::-1])
		return res[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		input = list(range(lo, hi + 1))
		output = []

		def getPower(val, currPower):
			if val == 1:
				output.append(currPower)
				return None
			elif val % 2 == 0:
				val /= 2
				currPower += 1
				getPower(val, currPower)
			else:
				val = 3 * val + 1
				currPower += 1
				getPower(val, currPower)
		outputDict = dict.fromkeys(input, 0)
		for num in input:
			getPower(num, 0)
		for (keys, vals) in enumerate(outputDict.keys()):
			outputDict[vals] = output[keys]
		outputDict = sorted(((value, key) for (key, value) in outputDict.items()))
		return outputDict[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		cache = {1: 0}

		def power(n):
			if n in cache:
				return cache[n]
			if n & 1:
				cache[n] = 1 + power(3 * n + 1)
				return cache[n]
			else:
				cache[n] = 1 + power(n // 2)
				return cache[n]
		out = []
		for i in range(lo, hi + 1):
			out.append([i, power(i)])
		out.sort(key=lambda x: x[1])
		return out[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def BFS(queue):
			while queue:
				(var, level) = queue.popleft()
				if var == 1:
					return level
				if var % 2:
					queue.append([3 * var + 1, level + 1])
				else:
					queue.append([var / 2, level + 1])
		ans = []
		for i in range(lo, hi + 1):
			ans.append((i, BFS(deque([[i, 0]]))))
		ans = sorted(ans, key=lambda l: l[1])
		return ans[k - 1][0]


def power_value(num: int, counter=0):
	if num % 2 == 0:
		num = num / 2
	else:
		num = 3 * num + 1
	counter += 1
	if num == 1:
		return counter
	else:
		return power_value(num, counter=counter)

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		to_sort = []
		for i in range(lo, hi + 1):
			to_sort.append([i, power_value(i)])
		to_sort = sorted(to_sort, key=lambda x: x[1])
		return to_sort[k - 1][0]


class Solution:

	def powerValue(self, n):
		count = 0
		while n != 1:
			if n % 2 == 0:
				n = n / 2
			else:
				n = 3 * n + 1
			count += 1
		return count

	def getKth(self, lo: int, hi: int, k: int) -> int:
		minHeap = []
		for i in range(lo, hi + 1):
			heapq.heappush(minHeap, (self.powerValue(i), i))
		i = 1
		while i < k:
			heapq.heappop(minHeap)
			i += 1
		return minHeap[0][1]


class Solution:

	def getKth(self, lo: int, hi: int, m: int) -> int:
		a = [i for i in range(lo, hi + 1)]
		z = []

		def cv(s, c, k):
			if s in k:
				k[s] = k[s] + 1
			elif s % 2 == 0:
				s = s / 2
				c = c + 1
			else:
				s = 3 * s + 1
				c = c + 1
			if s == 1:
				return (list(k.values()), c)
			return cv(s, c, k)
		for i in a:
			c = 0
			k = {}
			(b, f) = cv(i, c, k)
			z.append([sum(b) + f, i])
		z.sort(key=lambda x: x[0])
		a = []
		for i in z:
			a.append(i[1])
		return a[m - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def get_power_of_element(x):
			if x == 1:
				return 0
			elif x % 2 == 0:
				x = x / 2
				return 1 + get_power_of_element(x)
			elif x % 2 != 0:
				x = 3 * x + 1
				return 1 + get_power_of_element(x)
		array_of_numbers = [x for x in range(lo, hi + 1)]
		hash_map = {}
		for i in array_of_numbers:
			k_value = get_power_of_element(i)
			hash_map[i] = k_value
		array_of_values = [(y, x) for (x, y) in list(hash_map.items())]
		array_of_values.sort(key=lambda x: x[0])
		return array_of_values[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		p = {}
		for i in range(lo, hi + 1):
			temp = 0
			copy_i = i
			if copy_i == 1:
				p[i] = 0
			while copy_i != 1:
				if copy_i % 2 == 0:
					copy_i /= 2
					temp += 1
					if copy_i == 1:
						p[i] = temp
						break
				if copy_i % 2 != 0:
					copy_i = 3 * copy_i + 1
					temp += 1
					if copy_i == 1:
						p[i] = temp
						break
		print('p is')
		print(p)
		p = sorted(list(p.items()), key=lambda x: x[1])
		track = 0
		for ele in p:
			track += 1
			if track == k:
				return ele[0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		dic = {}
		for i in range(lo, hi + 1):
			z = self.getTheP(i)
			dic[i] = self.getTheP(i)
		return sorted(list(dic.items()), key=lambda x: (x[1], x[0]))[k - 1][0]

	def getTheP(self, q: int) -> int:
		Pow = 0
		while q != 1:
			if q % 2 == 0:
				q = q / 2
				Pow += 1
			else:
				q = 3 * q + 1
				Pow += 1
		return Pow


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		ans = []
		for x in range(lo, hi + 1):
			count = 0
			num = x
			while x > 1:
				if x % 2 == 0:
					x = x / 2
				else:
					x = 3 * x + 1
				count += 1
			heapq.heappush(ans, [count, num])
		return heapq.nsmallest(k, ans)[-1][-1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def getPower(n):
			return 0 if n == 1 else (getPower(3 * n + 1) if n % 2 else getPower(n / 2)) + 1
		return sorted(range(lo, hi + 1), key=getPower)[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		i = 0
		pow2Dict = {1: 0}
		pow2Now = 1
		while i < 32:
			i += 1
			pow2Now *= 2
			pow2Dict[pow2Now] = i
		visited = {}
		stack = [(0, i, i) for i in range(lo, hi + 1)]
		while stack:
			(stepNow, numNow, numOrigin) = heapq.heappop(stack)
			if numNow in pow2Dict:
				visited[numOrigin] = stepNow + pow2Dict[numNow]
			elif numNow in visited:
				visited[numOrigin] = stepNow + visited[numNow]
			elif numNow % 2:
				heapq.heappush(stack, (stepNow + 1, numNow * 3 + 1, numOrigin))
			else:
				heapq.heappush(stack, (stepNow + 1, numNow // 2, numOrigin))
		sortedNums = sorted([i for i in range(lo, hi + 1)], key=lambda x: (visited[x], x))
		return sortedNums[k - 1]


class Solution:

	def core(self, num: int, counter: int) -> int:
		if num == 1:
			return counter
		if num % 2 == 0:
			return self.core(num // 2, counter + 1)
		return self.core(num * 3 + 1, counter + 1)

	def getPowerValue(self, num: int) -> int:
		return self.core(num, 0)

	def generatePowerValues(self, lo: int, hi: int) -> List[int]:
		output = [0]
		if hi == 1:
			return output
		for i in range(2, hi + 1):
			if i % 2 == 0:
				output.append(1 + output[i // 2 - 1])
			else:
				output.append(3 + output[(3 * i + 1) // 4 - 1])
		return output[lo - 1:hi]

	def getKth(self, lo: int, hi: int, k: int) -> int:
		output = []
		for i in range(lo, hi + 1):
			output.append((i, self.getPowerValue(i)))
		output.sort(key=lambda x: (x[1], x[0]))
		return output[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power_dic = {}
		power_dic_sub = {}
		for i in range(lo, hi + 1):
			power_dic_sub[i] = self.getPower(i, 0, [], power_dic)
		result_tmp = sorted(power_dic_sub.items(), key=lambda kv: kv[1], reverse=False)
		return result_tmp[k - 1][0]

	def getPower(self, num, power, power_record, power_dic):
		if num == 1:
			for i in power_record:
				if not power_dic[i]:
					power_dic[i] = power - power_record.index(i)
			return power
		if num in power_dic:
			return power_dic[num]
		if num % 2 == 0:
			num = num / 2
		else:
			num = 3 * num + 1
		power += 1
		return self.getPower(num, power, power_record, power_dic)


class Solution:

	def getKth(self, a: int, b: int, k: int) -> int:

		def fun(x, d):
			if x == 1:
				return 0
			if x % 2 == 0:
				if x // 2 in d:
					d[x] = d[x // 2] + 1
				else:
					d[x] = fun(x // 2, d) + 1
			elif 3 * x + 1 in d:
				d[x] = d[3 * x + 1] + 1
			else:
				d[x] = fun(3 * x + 1, d) + 1
			return d[x]
		d = {}
		for i in range(a, b + 1):
			fun(i, d)
		d[1] = 0
		ans = []
		for i in range(a, b + 1):
			ans.append((d[i], i))
		ans.sort()
		return ans[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = {}

		def dp(x):
			if x == 1:
				return 0
			if x % 2:
				t = 3 * x + 1
				if t not in d:
					d[t] = dp(t)
				return 1 + d[t]
			else:
				t = x // 2
				if t not in d:
					d[t] = dp(t)
				return 1 + d[t]
		d1 = {}
		for i in range(lo, hi + 1):
			d1[i] = dp(i)
		return sorted(d1, key=lambda x: d1[x])[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		memo = {}

		def help(x):
			if x in memo:
				return memo[x]
			if x == 1:
				return 0
			if x % 2 == 0:
				memo[x] = 1 + help(x // 2)
			else:
				memo[x] = 1 + help(x * 3 + 1)
			return memo[x]
		return sorted(list(range(lo, hi + 1)), key=lambda x: [help(x), x])[k - 1]


class Solution:

	def getPowVal(self, x: int) -> int:
		if x in self.memo:
			return self.memo[x]
		newX = x // 2 if x % 2 == 0 else 3 * x + 1
		self.memo[x] = 1 + self.getPowVal(newX)
		return self.memo[x]

	def getKth(self, lo: int, hi: int, k: int) -> int:
		self.memo = {1: 0}
		powVal = [(x, self.getPowVal(x)) for x in range(lo, hi + 1)]
		powVal.sort(key=lambda x: x[1])
		return powVal[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		dp = dict()
		dp[0] = dp[2] = 1
		dp[1] = 0

		def calc(x):
			if dp.get(x) is not None:
				return dp.get(x)
			if x % 2 == 0:
				dp[x] = calc(x // 2) + 1
			else:
				dp[x] = calc(x * 3 + 1) + 1
			return dp[x]
		to_sort = []
		for i in range(lo, hi + 1):
			calc(i)
			to_sort.append([i, dp.get(i)])
		sorted_res = sorted(to_sort, key=lambda x: x[1])
		return sorted_res[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		res = []
		self.inc = {1: 0}
		while lo <= hi:
			heapq.heappush(res, (self.find_power(lo), lo))
			lo += 1
		for i in range(k):
			ans = heapq.heappop(res)[1]
		return ans

	def find_power(self, var):
		if var in self.inc:
			return self.inc[var]
		if var % 2 == 0:
			self.inc[var] = self.find_power(var // 2) + 1
		else:
			self.inc[var] = self.find_power(3 * var + 1) + 1
		return self.inc[var]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		memo = {1: 0}

		def getPower(x):
			if x in memo:
				return memo[x]
			if x % 2 == 0:
				memo.update({x: getPower(x // 2) + 1})
				return memo[x]
			else:
				memo.update({x: getPower(x * 3 + 1) + 1})
				return memo[x]
		return sorted(map(lambda x: (getPower(x), x), range(lo, hi + 1)))[k - 1][1]


class Solution:

	def getPower(self, n):
		if n == 1:
			return 0
		if n in self.dp:
			return self.dp[n]
		elif n % 2 == 0:
			self.dp[n] = self.getPower(n // 2) + 1
		else:
			self.dp[n] = self.getPower(3 * n + 1) + 1
		return self.dp[n]

	def getKth(self, lo: int, hi: int, k: int) -> int:
		tmp = []
		self.dp = {}
		for num in range(lo, hi + 1):
			tmp.append((num, self.getPower(num)))
		tmp.sort(key=lambda x: (x[1], x[0]))
		return tmp[k - 1][0]


import functools

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		return sorted(((get_power_value(x), x) for x in range(lo, hi + 1)))[k - 1][1]

@functools.lru_cache(maxsize=None)
def get_power_value(x):
	if x == 1:
		return 0
	return 1 + get_power_value(x / 2 if x % 2 == 0 else x * 3 + 1)


from collections import defaultdict

class Solution:

	def helper(self, x):
		if x == 2:
			return 1
		if x in self.table:
			return self.table[x]
		if x % 2:
			y = int(3 * x + 1)
		else:
			y = int(x / 2)
		ans = 1 + self.helper(y)
		self.table[x] = ans
		return ans

	def getKth(self, lo: int, hi: int, k: int) -> int:
		self.table = dict()
		self.lo = lo
		self.hi = hi
		powers = [self.helper(x) for x in range(lo, hi + 1)]
		tosort = list(zip(powers, list(range(lo, hi + 1))))
		return sorted(tosort)[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		ans = []
		self.dic = {1: 0}
		for i in range(lo, hi + 1):
			c = self.solvePower(i)
			ans.append([c, i])
		ans.sort()
		return ans[k - 1][1]

	def solvePower(self, num):
		if self.dic.get(num, None) != None:
			return self.dic[num]
		if num % 2 == 0:
			temp = self.solvePower(num // 2)
		else:
			temp = self.solvePower(num * 3 + 1)
		self.dic[num] = 1 + temp
		return self.dic[num]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power = {}
		power[1] = 0
		current = {}
		nums = list(range(lo, hi + 1))
		for i in nums:
			self.get_power_value(power, current, i)
		value = sorted(list(current.items()), key=lambda x: x[1])
		arr = list([x[0] for x in value])
		return arr[k - 1]

	def get_power_value(self, power, current, num):
		arr = []
		start = num
		if num in power:
			current[num] = power[num]
		else:
			arr = []
			value = num
			found_power = 0
			while value != 1:
				if value % 2 == 0:
					value /= 2
				else:
					value = value * 3 + 1
				arr.append(value)
				if value in power:
					found_power = power[value]
					break
			for i in range(0, len(arr)):
				power[start] = len(arr) - i + found_power
				start = arr[i]
			current[num] = power[num]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		@lru_cache(None)
		def power(x):
			if x == 1:
				return 0
			return 1 + power(x * 3 + 1) if x & 1 else 1 + power(x >> 1)
		a = [(power(x), x) for x in range(lo, hi + 1)]
		a.sort()
		print(a)
		return a[k - 1][1]


class Solution:

	def __init__(self):
		self.d = {}

	def solve(self, x):
		if x == 1:
			return 0
		if self.d.get(x, 0) != 0:
			return self.d[x]
		if x % 2 == 0:
			self.d[x] = 1 + self.solve(x // 2)
			return self.d[x]
		else:
			self.d[x] = 1 + self.solve(x * 3 + 1)
			return self.d[x]

	def getKth(self, lo, hi, k):
		ar = []
		for i in range(hi, lo - 1, -1):
			ar.append((self.solve(i), i))
		ar.sort()
		return ar[k - 1][1]


import heapq
from operator import itemgetter

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		memo = {1: 0, 2: 1}
		num_to_power = []
		for num in range(lo, hi + 1):
			if num == 1:
				num_to_power.append((num, 0))
				continue
			i = num
			steps = 0
			while i != 1:
				if i in memo:
					num_to_power.append((num, steps + memo[i]))
					memo[num] = steps + memo[i]
					i = 1
				elif i % 2 == 0:
					i = i // 2
					steps += 1
				else:
					i = 3 * i + 1
					steps += 1
		num_to_power = sorted(num_to_power, key=itemgetter(1, 0))
		return num_to_power[k - 1][0]


from collections import defaultdict
from operator import itemgetter

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power_dict = defaultdict(int)

		def cal_power(n):
			nonlocal power_dict
			if n in list(power_dict.keys()):
				return power_dict[n] - 1
			if n == 1:
				return 0
			if n % 2 == 0:
				n = n / 2
			elif n % 2 == 1:
				n = 3 * n + 1
			power_dict[n] = cal_power(n) + 1
			return power_dict[n]
		lst = []
		for i in range(lo, hi + 1):
			lst.append((cal_power(i), i))
		lst = sorted(lst, key=itemgetter(0))
		return lst[k - 1][1]


from collections import defaultdict

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		m = defaultdict(int)

		def do(n):
			if n == 1:
				return 0
			if m[n] != 0:
				return m[n]
			elif n % 2 == 0:
				m[n] = 1 + do(n / 2)
			else:
				m[n] = 1 + do(3 * n + 1)
			return m[n]
		res = []
		for i in range(lo, hi + 1):
			res.append([do(i), i])
		res.sort()
		return res[k - 1][1]


class Solution:
	cache = {}

	def getKth(self, lo: int, hi: int, k: int) -> int:
		l = list(range(lo, hi + 1))
		l.sort(key=lambda x: self.findKth(x))
		return l[k - 1]

	def findKth(self, n: int) -> int:
		if n in self.cache:
			return self.cache[n]
		if n == 1:
			return 0
		if n % 2 == 0:
			res = 1 + self.findKth(int(n / 2))
		else:
			res = 1 + self.findKth(3 * n + 1)
		self.cache[n] = res
		return res

class Solution_eva:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def calSteps(x):
			cnt = 0
			while x != 1:
				x = x / 2 if x % 2 == 0 else 3 * x + 1
				cnt += 1
			return cnt
		return sorted([ele for ele in range(lo, hi + 1)], key=lambda x: calSteps(x))[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		self.visited = {}

		def recur(n):
			if n in self.visited:
				return self.visited[n]
			if n == 1:
				return 0
			else:
				if n % 2 == 0:
					moves = 1 + recur(int(n / 2))
				else:
					moves = 1 + recur(int(3 * n) + 1)
				self.visited[n] = moves
				return self.visited[n]
		for i in range(hi, lo - 1, -1):
			if i not in self.visited:
				self.visited[i] = recur(i)
		result = [(x, self.visited[x]) for x in self.visited if lo <= x and x <= hi]
		result.sort(key=lambda x: (x[1], x[0]))
		return result[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power_list = []
		d = {}
		for i in range(lo, hi + 1):
			a = self.power(i, d)
			power_list.append(a)
		print(power_list)
		list2 = [i for i in range(lo, hi + 1)]
		list2 = [x for (x, y) in sorted(zip(list2, power_list), key=lambda x: x[1])]
		return list2[k - 1]

	def power(self, x, dict1):
		if x in dict1:
			print(('hi', x))
			return dict1[x]
		else:
			orig = x
			list1 = []
			count = 0
			while x != 1 and x not in dict1:
				if x % 2 == 0:
					x /= 2
				else:
					x = 3 * x + 1
				x = int(x)
				count += 1
				list1.append(x)
			n = len(list1)
			if x == 1:
				dict1[orig] = n
				for elem in list1:
					dict1[elem] = n - 1
					n -= 1
			else:
				print(('hi ', x))
				dict1[orig] = n + dict1[x]
				for elem in list1:
					dict1[elem] = n - 1 + dict1[x]
					n -= 1
			return dict1[orig]


class Heap:

	def __init__(self, initial=None, key=lambda x: x):
		self.key = key
		if initial:
			self._data = [(key(item), item) for item in initial]
			heapq.heapify(self._data)
		else:
			self._data = []

	def push(self, item):
		heapq.heappush(self._data, (self.key(item), item))

	def pop(self):
		return heapq.heappop(self._data)[1]

	def peek(self):
		return self._data[0][1]

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		powers = {}
		heap = Heap(key=lambda n: -self._get_power(n, powers))
		for n in range(lo, lo + k):
			heap.push(n)
		for n in range(lo + k, hi + 1):
			heap.push(n)
			heap.pop()
		return heap.peek()

	def _get_power(self, n: int, powers: dict) -> int:
		orig_n = n
		if n not in powers:
			power = 0
			while n != 1:
				if n % 2:
					n = n * 3 + 1
				else:
					n //= 2
				power += 1
				if n in powers:
					power += powers[n]
					break
			powers[orig_n] = power
		return powers[orig_n] - 1 / orig_n


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		steps = defaultdict(lambda : None)
		steps[1] = 0
		vals = list(range(lo, hi + 1))
		powers = []
		for v in vals:
			s = v
			num_steps = 0
			while s != 1:
				if steps[s] is not None:
					num_steps += steps[s]
					break
				if s % 2 == 0:
					s //= 2
				else:
					s = 3 * s + 1
				num_steps += 1
			steps[v] = num_steps
			powers.append(num_steps)
		items = sorted(zip(powers, vals))
		return items[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		memo = {}
		res = []
		for n in range(lo, hi + 1):
			power = 0
			x = n
			while x >= 1:
				if x == 1:
					memo[n] = power
					break
				elif x in memo:
					power += memo[x]
					memo[n] = power
					break
				elif x % 2 == 0:
					x //= 2
					power += 1
				elif x % 2 != 0:
					x = 3 * x + 1
					power += 1
		res = sorted(memo.items(), key=lambda kv: (kv[1], kv[0]))
		return res[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		@lru_cache(maxsize=None)
		def get_power(n):
			if n == 1:
				return 0
			elif n % 2:
				return 1 + get_power(3 * n + 1)
			return 1 + get_power(n // 2)
		nums = []
		for i in range(lo, hi + 1):
			nums.append([get_power(i), i])
		nums.sort()
		return nums[k - 1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		lst = {1: 0}
		num_list = []
		for i in range(lo, hi + 1):
			ans = 0
			while i != 1:
				if i in list(lst.keys()):
					ans = lst[i] + ans
					break
				else:
					num_list = num_list + [i]
					if i % 2:
						i = i * 3 + 1
						ans += 1
					else:
						i /= 2
						ans += 1
			for (ind, num) in enumerate(num_list):
				lst[num] = ans - ind
			num_list = []
		power_list = [(i, lst[i]) for i in range(lo, hi + 1)]
		power_list.sort(key=lambda x: x[1])
		return power_list[k - 1][0]


from heapq import heapify, heappop
cache = {1: 0}

def collatz(y):
	if y in cache:
		return cache[y]
	x = y
	steps = 1
	while x > 1:
		if x % 2 == 1:
			x = 3 * x + 1
		else:
			x //= 2
		if x in cache:
			ans = cache[x] + steps
			break
		steps += 1
	else:
		ans = steps
	cache[y] = ans
	return ans

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		powers = [(collatz(x), x) for x in range(lo, hi + 1)]
		heapify(powers)
		for _ in range(k):
			x = heappop(powers)
		return x[1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		memo = {}

		def power(n):
			if n == 1:
				return 0
			if n in memo:
				return memo[n]
			if n % 2 == 0:
				res = 1 + power(n / 2)
			else:
				res = 1 + power(3 * n + 1)
			memo[n] = res
			return res
		s = sorted(range(lo, hi + 1), key=power)
		return s[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = collections.defaultdict(int)
		d[1] = 0
		d[2] = 1

		def dfs(num):
			if num in d:
				return d[num]
			count = 0
			if num % 2:
				d[num] = 1 + dfs(num * 3 + 1)
				return 1 + dfs(num * 3 + 1)
			if not num % 2:
				d[num] = 1 + dfs(num // 2)
				return 1 + dfs(num // 2)
		res = collections.defaultdict(int)
		for n in range(lo, hi + 1):
			res[n] = dfs(n)
		res = sorted(list(res.items()), key=lambda x: x[1])
		return res[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		power = {}
		for x in range(lo, hi + 1):
			power[x] = self._get_power(x, power)
		return sorted(power, key=power.get)[k - 1]

	def _get_power(self, x, power):
		if x in power:
			return power[x]
		if x == 1:
			return 0
		if x % 2 == 0:
			return self._get_power(x // 2, power) + 1
		else:
			return self._get_power(3 * x + 1, power) + 1


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		a = {}

		def check(n, a):
			ct = 0
			while n != 1:
				if n % 2 == 0:
					n = n / 2
				else:
					n = 3 * n + 1
				if n in a:
					ct += a[n] + 1
					return ct
					break
				ct += 1
			return ct
		for i in range(lo, hi + 1):
			a[i] = check(i, a)
		b = sorted(a.items(), key=lambda kv: (kv[1], kv[0]))
		return b[k - 1][0]


import heapq

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		pv_map = {}

		def pv(val):
			v = val
			cnt = 1
			while val != 1:
				if val in pv_map:
					pv_map[v] = cnt + pv_map[val] - 1
					return pv_map[v]
				if val % 2 == 0:
					val /= 2
				else:
					val = 3 * val + 1
				cnt += 1
			pv_map[v] = cnt
			return cnt
		h = []
		for v in range(lo, hi + 1):
			p = pv(v)
			if len(h) < k:
				heapq.heappush(h, (-p, -v))
			elif p < -h[0][0]:
				heapq.heapreplace(h, (-p, -v))
		return -h[0][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		@lru_cache(None)
		def p(x):
			if x == 1:
				return 0
			elif x & 1:
				return p(3 * x + 1) + 1
			else:
				return p(x >> 1) + 1
		return sorted(range(lo, hi + 1), key=p)[k - 1]


from functools import lru_cache
from heapq import heappop, heappush

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		@lru_cache(None)
		def get_steps(num):
			if num == 1:
				return 0
			elif num % 2:
				return 1 + get_steps(3 * num + 1)
			else:
				return 1 + get_steps(num // 2)
		pq = []
		for i in range(lo, hi + 1):
			heappush(pq, (-get_steps(i), -i))
			if len(pq) > k:
				heappop(pq)
		return -min(pq)[1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		if lo == hi == k == 1:
			return 1
		dic = {}

		def fun(n, count):
			if n == 1:
				return count
			count += 1
			if n % 2 == 0:
				n //= 2
			else:
				n = n * 3 + 1
			if n in dic:
				return count + dic[n]
			return fun(n, count)
		ans = []
		for i in range(lo, hi + 1):
			dic[i] = fun(i, 0)
		return sorted(list(dic.items()), key=lambda x: x[1])[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		if lo == 1 and hi == 1 and (k == 1):
			return 1
		memo = {}

		def count_steps(x, count, memo):
			if x == 1:
				return count
			count += 1
			if x % 2 == 0:
				x = x // 2
			else:
				x = 3 * x + 1
			if x in memo:
				return count + memo[x]
			return count_steps(x, count, memo)
		for x in range(lo, hi + 1):
			memo[x] = count_steps(x, 0, memo)
		return sorted(memo.items(), key=lambda x: x[1])[k - 1][0]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		memo = {}

		def num_steps(num):
			if num == 1:
				return 0
			elif num in memo:
				return memo[num]
			if num % 2 == 0:
				memo[num] = num_steps(num / 2) + 1
			else:
				memo[num] = num_steps(num * 3 + 1) + 1
			return memo[num]
		vals = []
		for i in range(lo, hi + 1):
			vals.append((i, num_steps(i)))
		vals = sorted(vals, key=lambda x: (x[1], x[0]))
		print(vals)
		vals = [i for (i, j) in vals]
		return vals[k - 1]


class Solution:

	def __recur(self, dp, num):
		if num in dp:
			return dp[num]
		res = 0
		if num % 2 == 0:
			res = self.__recur(dp, int(num / 2)) + 1
		else:
			res = self.__recur(dp, int(num * 3) + 1) + 1
		dp[num] = res
		return res

	def getKth(self, lo: int, hi: int, k: int) -> int:
		dp = {1: 0}
		for num in range(1, 1001):
			self.__recur(dp, num)
		power_order = sorted([(dp[key], key) for key in dp if key >= lo and key <= hi])
		return power_order[k - 1][1]


class Solution:

	def num_count(self, x, count):
		if x == 1:
			return count
		count += 1
		if x % 2 == 0:
			x = x // 2
		else:
			x = x * 3 + 1
		if x in self.dp:
			return count + self.dp[x]
		return self.num_count(x, count)

	def getKth(self, lo: int, hi: int, k: int) -> int:
		self.dp = {}
		for x in range(lo, hi + 1):
			self.dp[x] = self.num_count(x, 0)
		return sorted(self.dp.items(), key=lambda x: x[1])[k - 1][0]


class Solution:

	def power(self, memo, num):
		if num in memo:
			return memo[num]
		result = 0
		if num % 2 == 0:
			result = self.power(memo, int(num / 2)) + 1
		else:
			result = self.power(memo, int(num * 3) + 1) + 1
		memo[num] = result
		return result

	def getKth(self, lo: int, hi: int, k: int) -> int:
		memo = {1: 0}
		for num in range(1, 1001):
			self.power(memo, num)
		porder = sorted([(memo[key], key) for key in memo if key >= lo and key <= hi])
		return porder[k - 1][1]


class Solution:

	def __recur(self, dp, num):
		if num in dp:
			return dp[num]
		if num == 1:
			return 0
		res = 0
		if num % 2 == 0:
			res = self.__recur(dp, int(num / 2)) + 1
		else:
			res = self.__recur(dp, int(num * 3) + 1) + 1
		dp[num] = res
		return res

	def getKth(self, lo: int, hi: int, k: int) -> int:
		dp = {}
		dp[1] = 0
		dp[2] = 1
		for i in range(1, 1001):
			self.__recur(dp, i)
		temp = [(dp[key], key) for key in dp if key >= lo and key <= hi]
		temp.sort()
		return temp[k - 1][1]


dp = {}

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		result = [(num, self.getPowerValue(num)) for num in range(lo, hi + 1)]
		result.sort(key=lambda x: (x[1], x[0]))
		return result[k - 1][0]

	def getPowerValue(self, num) -> int:
		if num == 1:
			return 0
		if num in dp:
			return dp[num]
		if num % 2 == 0:
			dp[num] = 1 + self.getPowerValue(num / 2)
		else:
			dp[num] = 1 + self.getPowerValue(3 * num + 1)
		return dp[num]


class Solution:

	def __init__(self):
		self.cache = {1: 0, 2: 1, 3: 7, 4: 2, 5: 5, 6: 8, 7: 16, 8: 3}

	def getPower(self, n):
		steps = 0
		rem = n % 8
		if rem == 0:
			n = n // 8
			steps = 3
		elif rem == 1:
			n = n // 8 * 9 + 2
			steps = 5
		elif rem == 2:
			n = n // 8 * 3 + 1
			steps = 4
		elif rem == 3:
			n = n // 8 * 9 + 4
			steps = 5
		elif rem == 4 or rem == 5:
			n = n // 8 * 3 + 2
			steps = 4
		elif rem == 6:
			n = n // 8 * 9 + 8
			steps = 5
		else:
			n = n // 8 * 27 + 26
			steps = 6
		if n <= 8:
			return self.cache[n] + steps
		else:
			return self.getPower(n) + steps

	def getKth(self, low, high, k):
		data = [self.getPower(i) for i in range(low, high + 1)]
		sorted_data = sorted(zip(data, list(range(len(data)))), key=lambda x: x[0])
		return sorted_data[k - 1][1] + low


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		dp = defaultdict(int)
		dp[1] = 0

		def go(i):
			if i == 1:
				return 0
			if dp[i] > 0:
				return dp[i]
			if i % 2 == 0:
				ans = go(i // 2) + 1
			else:
				ans = go(3 * i + 1) + 1
			dp[i] = ans
			return ans
		for i in range(lo, hi + 1):
			dp[i] = go(i)
		lis = []
		for i in range(lo, hi + 1):
			lis.append((dp[i], i))
		lis.sort()
		ans = lis[k - 1]
		return ans[1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		def powerof(num, memo):
			step = 0
			n = num
			while n > 1:
				if n in memo:
					return step + memo[n]
				if n % 2 == 0:
					n = n // 2
				else:
					n = 3 * n + 1
				step += 1
			memo[num] = step
			return step
		mheap = []
		memo = {}
		for n in range(lo, hi + 1):
			mheap.append([powerof(n, memo), n])
		heapq.heapify(mheap)
		return heapq.nsmallest(k, mheap)[-1][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		d = {}

		def getPowerValue(x):
			if x in d:
				return d[x]
			steps = 0
			original = x
			while x != 1:
				if x % 2:
					x = 3 * x + 1
				else:
					x /= 2
				steps += 1
				if x in d:
					steps += d[x]
					break
			d[original] = steps
			return steps
		return sorted([x for x in range(lo, hi + 1)], key=getPowerValue)[k - 1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		h = {}
		heap = []
		for i in range(lo, hi + 1):
			print(i)
			q = deque()
			q.append((0, i))
			while q:
				x = q.popleft()
				if x[1] == 1 or x[1] in h:
					xx = x[0]
					if x[1] in h:
						xx += h[x[1]]
					if i not in h:
						h[i] = xx
					if len(heap) < k:
						heapq.heappush(heap, (-xx, -i))
					elif -xx > heap[0][0]:
						heapq.heappop(heap)
						heapq.heappush(heap, (-xx, -i))
					break
				if x[1] % 2 == 0:
					q.append((x[0] + 1, x[1] // 2))
				else:
					q.append((x[0] + 1, 3 * x[1] + 1))
		return -heap[0][1]


class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		@lru_cache
		def getPower(x):
			if x == 1:
				return 0
			if x % 2 == 0:
				return 1 + getPower(x // 2)
			return 1 + getPower(3 * x + 1)
		return sorted([(getPower(x), x) for x in range(lo, hi + 1)])[k - 1][1]


from functools import lru_cache

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		@lru_cache
		def getPower(x: int) -> int:
			if x == 1:
				return 1
			if x % 2 == 0:
				return getPower(x // 2) + 1
			if x % 2 == 1:
				return getPower(3 * x + 1) + 1
		powers = [0] * (hi - lo + 1)
		if len(powers) == 1:
			return lo
		for i in range(len(powers)):
			if i + lo != 1:
				powers[i] = getPower(i + lo) - 1
			else:
				powers[i] = getPower(i + lo)
		idxs = sorted(range(len(powers)), key=lambda x: powers[x])
		return lo + idxs[k - 1]


from functools import lru_cache

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:

		@lru_cache
		def power(n):
			if n == 1:
				return 0
			if n % 2 == 0:
				return 1 + power(n // 2)
			else:
				return 1 + power(3 * n + 1)
		powers = [(power(n), n) for n in range(lo, hi + 1)]
		powers.sort()
		return powers[k - 1][1]


class Solution:

	def power(self, n):
		c = 0
		while n != 1:
			if n % 2:
				n = n * 3 + 1
			else:
				n //= 2
			c += 1
		return c

	def getKth(self, lo: int, hi: int, k: int) -> int:
		e = [i for i in range(lo, hi + 1)]
		e.sort(key=self.power)
		return e[k - 1]


import heapq

class Solution:

	def getKth(self, lo: int, hi: int, k: int) -> int:
		memo = {}
		q = []
		for num in range(lo, hi + 1):
			count = 0
			tmp = num
			while num != 1:
				if num not in memo:
					if num % 2 == 0:
						cal = num // 2
					else:
						cal = 3 * num + 1
					memo[num] = cal
				num = memo[num]
				count += 1
			heapq.heappush(q, (count, tmp))
		while k > 0:
			item = heapq.heappop(q)
			k -= 1
		return item[1]