The power of an integer $x$ is defined as the number of steps required to transform $x$ into $1$ by repeatedly applying the following operations:

• If $x$ is even, then $x = x / 2$

• If $x$ is odd, then $x = 3 imes x + 1$

Given three integers lo, hi, and k, sort all integers in the inclusive range $[$lo, hi$]$ in ascending order based on their power value. If two or more integers have identical power values, sort them in ascending numerical order.

Return the $k$-th integer ($1$ indexed) in the sorted range.

Constraints:

• $1 \leq$ lo $\leq$ hi $\leq 1000$

• $1 \leq$ k $\leq$ hi $-$ lo $+ 1$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.