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 Ruby (2.7.1) (judge verdict: Accepted)

class Problem
  attr_accessor *(?a..?z).to_a.map(&:to_sym)

  def initialize
    @n, @k = gets.to_s.split.map { |v| v.to_i }
  end

  def solve
    eat(n, k)
  end

  def eat(n, k)
    x = length(n)
    case k
    when 0; 0
    when x; meat(n)
    when x + 1; meat(n) + 1
    when ->k { k < x }; eat(n - 1, k - 1)
    when ->k { k > x + 1 }; meat(n) + 1 + eat(n, k - x - 1)
    end
  end

  def show(ans)
    puts ans
  end

  def length(i); 2 ** (i + 2) - 3; end
  def meat(i); 2 ** (i + 1) - 1; end
end

Problem.new.instance_eval do
  show(solve)
end