E. Vlad and an Odd Ordering
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.
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.

Example
Input
11
7 1
7 2
7 3
7 4
7 5
7 6
7 7
1 1
34 14
84 19
1000000000 1000000000
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 $$$1$$$, $$$3$$$, $$$5$$$, $$$7$$$, $$$2$$$, $$$6$$$, $$$4$$$.