1926E · Vlad and an Odd Ordering

Problem: 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.

Input Format: 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.

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

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.