Vladislav has $$$n$$$ cards numbered $$$1, 2, \dots, n$$$. He wants to lay them down in a row as follows:
- First, he lays down all the odd-numbered cards from smallest to largest.
- Next, he lays down all cards that are twice an odd number from smallest to largest (i.e. $$$2$$$ multiplied by an odd number).
- Next, he lays down all cards that are $$$3$$$ times an odd number from smallest to largest (i.e. $$$3$$$ multiplied by an odd number).
- Next, he lays down all cards that are $$$4$$$ times an odd number from smallest to largest (i.e. $$$4$$$ multiplied by an odd number).
- And so on, until all cards are laid down.
What is the $$$k$$$-th card he lays down in this process? Once Vladislav puts a card down, he cannot use that card again.
Output
For each test case, output a single integer — the $$$k$$$-th card Vladislav lays down.
Example
Output
1
3
5
7
2
6
4
1
27
37
536870912
Note
In the first seven test cases, $$$n=7$$$. Vladislav lays down the cards as follows:
- First — all the odd-numbered cards in the order $$$1$$$, $$$3$$$, $$$5$$$, $$$7$$$.
- Next — all cards that are twice an odd number in the order $$$2$$$, $$$6$$$.
- Next, there are no remaining cards that are $$$3$$$ times an odd number. (Vladislav has only one of each card.)
- Next — all cards that are $$$4$$$ times an odd number, and there is only one such card: $$$4$$$.
- There are no more cards left, so Vladislav stops.
Thus the order of cards is $$$1$$$, $$$3$$$, $$$5$$$, $$$7$$$, $$$2$$$, $$$6$$$, $$$4$$$.