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)

#再起関数を使ったのが以下のもの、defで定義して漸化式を使う
#レベル N バーガーの下から X 層に含まれるパティの枚数」を f(N,X)とおく
n,x = gets.strip.split.map(&:to_i)
def f(n,x)
  if n==0
    return 1
  else
    if x==1
      return 0
    elsif 2<=x && x<=2**(n+1)-2
      return f(n-1,x-1)
    elsif x==2**(n+1)-1
      return f(n-1,x-2)+1
    elsif 2**(n+1)<=x && x<=2**(n+2)-4
      return f(n-1,2**(n+1)-3)+1+f(n-1,x-2**(n+1)+1)
    else
      return 2*f(n-1,2**(n+1)-3)+1
    end
  end
end
puts f(n,x)