1387\. Sort Integers by The Power Value

Medium

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 <code>k<sup>th</sup></code> 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.

**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 = 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.

**Constraints:**

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