The power of an integer x is defined as the number of steps needed to transform x into 1 using the following steps:
x is even then x = x / 2x is odd then x = 3 * x + 1For 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 kth 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 a 32-bit signed integer.
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Example 1:
\n\n\nInput: lo = 12, hi = 15, k = 2\nOutput: 13\nExplanation: The power of 12 is 9 (12 --> 6 --> 3 --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1)\nThe power of 13 is 9\nThe power of 14 is 17\nThe power of 15 is 17\nThe interval sorted by the power value [12,13,14,15]. For k = 2 answer is the second element which is 13.\nNotice that 12 and 13 have the same power value and we sorted them in ascending order. Same for 14 and 15.\n\n\n
Example 2:
\n\n\nInput: lo = 7, hi = 11, k = 4\nOutput: 7\nExplanation: The power array corresponding to the interval [7, 8, 9, 10, 11] is [16, 3, 19, 6, 14].\nThe interval sorted by power is [8, 10, 11, 7, 9].\nThe fourth number in the sorted array is 7.\n\n\n
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Constraints:
\n\n1 <= lo <= hi <= 10001 <= k <= hi - lo + 1我们将整数 x 的 权重 定义为按照下述规则将 x 变成 1 所需要的步数：
x 是偶数，那么 x = x / 2x 是奇数，那么 x = 3 * x + 1比方说，x=3 的权重为 7 。因为 3 需要 7 步变成 1 （3 --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1）。
\n\n给你三个整数 lo， hi 和 k 。你的任务是将区间 [lo, hi] 之间的整数按照它们的权重 升序排序 ，如果大于等于 2 个整数有 相同 的权重，那么按照数字自身的数值 升序排序 。
请你返回区间 [lo, hi] 之间的整数按权重排序后的第 k 个数。
注意，题目保证对于任意整数 x （lo <= x <= hi） ，它变成 1 所需要的步数是一个 32 位有符号整数。
\n\n
示例 1：
\n\n\n输入：lo = 12, hi = 15, k = 2\n输出：13\n解释：12 的权重为 9（12 --> 6 --> 3 --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1）\n13 的权重为 9\n14 的权重为 17\n15 的权重为 17\n区间内的数按权重排序以后的结果为 [12,13,14,15] 。对于 k = 2 ，答案是第二个整数也就是 13 。\n注意，12 和 13 有相同的权重，所以我们按照它们本身升序排序。14 和 15 同理。\n\n\n
示例 2：
\n\n\n输入：lo = 7, hi = 11, k = 4\n输出：7\n解释：区间内整数 [7, 8, 9, 10, 11] 对应的权重为 [16, 3, 19, 6, 14] 。\n按权重排序后得到的结果为 [8, 10, 11, 7, 9] 。\n排序后数组中第 4 个数字为 7 。\n\n\n
\n\n
提示：
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