This approach involves using a queue to simulate the process of revealing cards in increasing order. The given deck is first sorted to achieve this order. We then place the lowest cards at the positions where they will eventually be revealed.

The process is as follows:

1. Sort the deck.
2. Initialize an empty queue and the result deck with the same size as the input deck.
3. Place the indices of the result deck into the queue.
4. Iterate over the sorted deck; for every card, dequeue two indices (one for placing the card and another for recycling the top card to the bottom of the deck).

The card is placed at the index dequeued first, and after checking if there are still indices left, the second index is enqueued to the queue for the recycling process.

Consider using a mathematical pattern to determine the correct order of cards. Start by handling small cases and rebalance the reordering according to the general steps defined. This approach focuses on finding the sequence by mathematical induction, considering the card's positions multiplication pattern to simulate the reveal process. Given the position pos[i], the card is added during the iteration, assume it follows a position pattern according to pos[i - 2 ^ {k-t}].