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.

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

Vlad and an Odd Ordering

Examples