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;
using System.Collections.Generic;
class Program
{
  static long putty=0;
  static long eat=0;
  static void Main(string[] args)
  {
    var split = Console.ReadLine().Split(' ');
    int level = int.Parse(split[0]);
    eat = long.Parse(split[1]);
    
    eatBurger(level);
        
    Console.WriteLine(putty);
  }
  
  static void eatBurger(int level){
    if(level == 0){      
      putty++;
      eat--;
      return;
    }
    
    var puttyL = Math.Pow(2, level+1)-1;
    var eatL = (Math.Pow(2, level+1)-1)*2-1;
    if(eatL<eat){
      putty += (long)puttyL;
      eat -= (long)eatL;
      return;
    }
    
    eat--;
    if(eat<=0) return;

    eatBurger(level-1);
    if(eat<=0) return;
  
    putty++;
    eat--;
    if(eat<=0) return;

    eatBurger(level-1);
    if(eat<=0) return;

    eat--;
    if(eat<=0) return;
  }
}