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 (2.3.3) (judge verdict: Accepted)

n, x = gets.strip.split.map(&:to_i)

@p_counts = [1]
@b_counts = [0]

n.times do 
  @p_counts.push(@p_counts.last*2+1)
  @b_counts.push(@b_counts.last*2+2)
end
@pb_counts = @p_counts.zip(@b_counts).map {|l, r| l+r }

#p @p_counts
#p @b_counts
#p @pb_counts

def bite_count(dim, count)
  if dim.zero?
    if count <= 0
      return 0
    else
      return 1
    end
  end

  return bite_count(dim-1, count-1) if count <= 1 + @pb_counts[dim-1]
  @p_counts[dim-1] +1 + bite_count(dim-1, count-1-@pb_counts[dim-1]-1)
end

p bite_count(n, x)