101153: [AtCoder]ABC115 D - Christmas

Problem Statement

In some other world, today is Christmas.

Mr. Takaha decides to make a multi-dimensional burger in his party. A level-$L$ burger ($L$ is an integer greater than or equal to $0$) is the following thing:

• A level-$0$ burger is a patty.
• A level-$L$ burger $(L \geq 1)$ is a bun, a level-$(L-1)$ burger, a patty, another level-$(L-1)$ burger and another bun, stacked vertically in this order from the bottom.

For example, a level-$1$ burger and a level-$2$ burger look like BPPPB and BBPPPBPBPPPBB (rotated $90$ degrees), where B and P stands for a bun and a patty.

The burger Mr. Takaha will make is a level-$N$ burger. Lunlun the Dachshund will eat $X$ layers from the bottom of this burger (a layer is a patty or a bun). How many patties will she eat?

Constraints

• $1 \leq N \leq 50$
• $1 \leq X \leq ($ the total number of layers in a level-$N$ burger $)$
• $N$ and $X$ are integers.

Input

Input is given from Standard Input in the following format:

$N$ $X$

Output

Print the number of patties in the bottom-most $X$ layers from the bottom of a level-$N$ burger.

Sample Input 1

2 7

Sample Output 1

4

There are $4$ patties in the bottom-most $7$ layers of a level-$2$ burger (BBPPPBPBPPPBB).

Sample Input 2

1 1

Sample Output 2

0

The bottom-most layer of a level-$1$ burger is a bun.

Sample Input 3

50 4321098765432109

Sample Output 3

2160549382716056

A level-$50$ burger is rather thick, to the extent that the number of its layers does not fit into a $32$-bit integer.