CF1926E 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 $ .