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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
//using System.Linq;
class Program
{
  //static List<string> list;
	static void Main(string[] args)
	{
		// 入力フェーズ
        string[] input = Console.ReadLine().Split(' ');
        int N = int.Parse(input[0]);
        long X = long.Parse(input[1]);

        long ret = fullEat(N,X);


    // 出力
        Console.WriteLine(ret);
    }
		class layer{ //自作クラス
			public long total {set; get;} // 全部の層数
			public long paty {set; get;}  // パティの数
      public long banz {set; get;}  // バンズの数
		}
    static private long fullEat(int N, long X)
    {
      // レベル1バーガーは BPPPBでそれ以上小さくできない
      if(N == 1)
      {
        long ret = 0;
        if(X == 5) ret = X - 2;
        else ret = X - 1;
        return ret;
      }
      // 食べきったパティの数を返す
      if(X <= 1)
      {
        // 一番外側のバンズも食べられない
        return 0;
      }
      layer burger = getLayerNum(N);
      if(burger.total == X)
      {
        //レベルNバーガーをちょうど食べきった
        return burger.paty;
      }

      if(X == (burger.total-3)/2 + 1)
      {
        // レベルN-1バーガーと、一番外側のバンズを食べた
        return getLayerNum(N-1).paty;
      }else if(X == (burger.total-3)/2 + 2)
      {
        // バンズ・レベルN-1バーガー・パティを食べた
        return getLayerNum(N-1).paty + 1;
      }else if(X > (burger.total-3)/2 + 2)
      {
        // バンズ・レベルN-1バーガー・パティを食べて、さらにN-1バーガーの一部を食べる
        layer burger_s = getLayerNum(N-1);
        long eated = burger_s.paty + 1;
        long rest = X - (burger_s.total + 2);
        return eated + fullEat(N-1, rest);
      }else
      {
        // レベルN-1バーガーも食べきれなかったので、一番外側のバンズを食べて、レベルN-1バーガーの一部を食べる
        return fullEat(N-1, X-1);
      }
    }

    static private layer getLayerNum(int N)
    {
      layer ret = new layer();
      // 全部で 2^(N+2)-3層、パティは2^(N+1)-1, バンズは2^(N+1)-2
      long power = (long)Math.Pow(2, N+1);
      ret.total = power*2 - 3;
      ret.paty = power -1;
      ret.banz = power -2;
      return ret;
    }


}