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: Time Limit Exceeded)

if !ENV['RUBY_THREAD_VM_STACK_SIZE']
  exec({'RUBY_THREAD_VM_STACK_SIZE'=>'1000000000'}, '/usr/bin/ruby', $0)
else
  # util functions

  # debug
  $debugFlag = ( ARGV[0] != nil )
  p "==== DEBUG MODE ====" if $debugFlag

  def pd(str)
    p str if $debugFlag
  end

  def printd(str)
    print str if $debugFlag
  end

  # input
  inputs = []
  lc = 0
  while l = $stdin.gets do
    if false
      inputs << l.chomp.split(" ").map(&:to_s)
    else
      inputs << l.chomp.split(" ").map(&:to_i)
    end
    lc += 1
  end

  nn = inputs[0][0]
  xx = inputs[0][1]

  # input check
  if $debugFlag
    p "--- INPUT (begin) ---"
    inputs.each do |l_i|
      p l_i
    end
    p "--- INPUT (end) ---"
    print "\n"
  end

  # body
  if $debugFlag
    p nn
    p xx
  end

  def rec(n, x)
    if x == 0
      return 0
    end
    if x == 1 and n == 0
      return 1
    end
    
    n_layer = 2**(n+2) - 3
    buf = 0
    xp = x
    if x >= (n_layer - 3)/2 + 2
      buf += 2**n
      xp = x - ((n_layer - 3)/2 + 2)
    else
      xp = x - 1
    end

    return buf + rec(n - 1, xp)
  end

  puts rec(nn, xx)
end