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.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		string[] input = Console.ReadLine().Split(' ');
		long n = long.Parse(input[0]);
		long x = long.Parse(input[1]);
    long answer = 0;
    long lookNum = n;

    long[] allCount = new long[51];
    long[] patyCount = new long[51];
    
    allCount[0] = 1;
    patyCount[0] = 1;
    for(int i = 1; i <= 50; i++)
    {
      allCount[i] = 2*allCount[i-1] + 3;
      patyCount[i] = 2*patyCount[i-1] + 1;
    }

    while(true)
    {  
      if(x <= 1 && lookNum > 0) break;
      if(lookNum == 0)
      {
        if(x == 1) answer++;
        break;
      }
      
      if(x < allCount[lookNum]/2+1)
      {
        x--;
        lookNum--;
        continue;
      }
      else if(x == allCount[lookNum]/2+1)
      {
        x -= 2;//左と中央を除く
        lookNum--;
        answer++;
        continue;
      }
      else if(x < allCount[lookNum])
      {
        //Console.WriteLine("a");
        x -= 2;
        x -= allCount[lookNum-1];
        answer++;
        answer += patyCount[lookNum-1];
        lookNum--;
        //Console.WriteLine(answer);
        continue;
      }else
      {
        answer += patyCount[lookNum];
        break;
      }
      
    }

		Console.WriteLine(answer);
	}
}