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.split.map(&:to_i)
# n, x = 2, 8

# require 'tapp'
# [n, x].tapp
@memo = {}
@memo[0] = [1, 1]
def trav(level, rest)
  # [level, rest].tapp
  if @memo[level] && @memo[level][0] <= rest
    return @memo[level]
  end

  eaten_total = 0
  forward_total = 0

  forward_total += 1
  rest -= 1
  if rest == 0
    return [forward_total, eaten_total]
  end

  forward, eaten = trav(level - 1, rest)
  forward_total += forward
  rest -= forward
  eaten_total += eaten
  if rest == 0
    return [forward_total, eaten_total]
  end

  forward_total += 1
  rest -= 1
  eaten_total += 1
  if rest == 0
    return [forward_total, eaten_total]
  end

  forward, eaten = trav(level - 1, rest)
  forward_total += forward
  rest -= forward
  eaten_total += eaten
  if rest == 0
    return [forward_total, eaten_total]
  end

  forward_total += 1
  rest -= 1

  @memo[level] = [forward_total, eaten_total]

  return [forward_total, eaten_total]
end

# n = 2
# x = 7
forward, eaten = trav(n, x)
puts eaten