In an infinite complete binary tree, nodes are labeled in a zigzag order across consecutive levels:

• The first level contains the root with label $1$.

• The second level contains nodes labeled $3$ to $2$ from left to right.

• The third level contains nodes labeled $4$ to $7$ from left to right.

• The fourth level contains nodes labeled $15$ to $8$ from left to right, and so on, reversing direction at each level.

Given the label of a node in this tree, return a list of labels representing the path from the root to the node with the given label.

Constraints:

• $1 \le label \le 10^6$

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.