Christmas

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.

Examples

Input

2 7

Output

4

Input

1 1

Output

0

Input

50 4321098765432109

Output

2160549382716056

inputFormat

Input

Input is given from Standard Input in the following format:

N X

outputFormat

Output

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

Examples

Input

2 7

Output

4

Input

1 1

Output

0

Input

50 4321098765432109

Output

2160549382716056

样例

50 4321098765432109

2160549382716056