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)

@layer = [1]
@meat = [1]
1.upto(N) do |i|
  @layer[i] = @layer[i - 1] * 2 + 3
  @meat[i] = @meat[i - 1] * 2 + 1
end

def search(n, x)
  return 0 if x <= 0
  return 1 if n == 0 && x == 1
  if x <= @layer[n - 1] + 1
    return search(n - 1, x - 1)
  elsif x == @layer[n - 1] + 2
    return @meat[n - 1] + 1
  elsif x <= @layer[n - 1] * 2 + 2
    return @meat[n - 1] + 1 + search(n - 1, x - @layer[n - 1] - 2)
  else
    return @meat[n - 1] * 2 + 1
  end
end

puts search(N, X)