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)

def burger(i)
  if i == 0
    'P'
  else
    'B' + burger(i-1) + 'P' + burger(i-1) + 'B'
  end
end

def burger_num(level, x)
  return 1 if level == 0
  if @hb.has_key?(level)
    return @hb[level][0..x-1].count('P')
  end

  prev_level_size = @h[level-1]
  if x == 0
    0
  elsif x == prev_level_size + 2
    burger_num(level-1, prev_level_size) + 1
  elsif x == @h[level]
    burger_num(level-1, prev_level_size) * 2 + 1
  elsif x < prev_level_size + 2
    burger_num(level-1, x-1)
  else
    burger_num(level-1, prev_level_size) + 1 + burger_num(level-1, x-2-prev_level_size)
  end
end

n, x = gets.split.map(&:to_i)
q = 1
@h = {0=>q}
@hb = {0=>'P'}
(1..n).each do |i|
  q = 3 + q*2
  @h[i] = q
  @hb[i] = burger(i) if i < 15
end

puts burger_num(n, x)