Problem:
Score : 400 points

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.

Solution in PHP (5.6.30) (judge verdict: Time Limit Exceeded)

<?php
  fscanf(STDIN, "%d %d", $level,$layers);
	// fscanf(STDIN, "", $layers);
	$burger = constructBurger($level);
	$burger_char_array = str_split($burger);
	$count = 0;
	for($i = 0; $i<$layers ; $i++){
    	if(sizeof($burger_char_array) < $i)break;
      	if($burger_char_array[$i] == 'P') $count++;
    }
	echo $count;

function constructBurger($burger){
	if($burger == 0){
      return 'P';
    }else{
     return 'B'.constructBurger($burger-1).'P'. constructBurger($burger-1).'B';
    }


}

?>