A11347. Vlad and an Odd Ordering

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.

The first line contains an integer $t$ ( $1 \leq t \leq 5 \cdot 10^4$ ) — the number of test cases.

The only line of each test case contains two integers $n$ and $k$ ( $1 \leq k \leq n \leq 10^9$ ) — the number of cards Vlad has, and the position of the card you need to output.

For each test case, output a single integer — the $k$ -th card Vladislav lays down.

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 $1$ , $3$ , $5$ , $7$ , $2$ , $6$ , $4$ .