Vlad and an Odd Ordering
Description
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.
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.
Input
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
For each test case, output a single integer — the $k$-th card Vladislav lays down.
11
7 1
7 2
7 3
7 4
7 5
7 6
7 7
1 1
34 14
84 19
1000000000 1000000000
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.