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: Runtime Error)

using System;
 
class Sample{
  	public static String MakeBurger(int high,String Burger){
      for(int i=0;i<high;i++){
          Burger="B"+Burger+"P"+Burger+"B";
      }
      return Burger;
    }
  	// 文字の出現回数をカウント
  public static long CountChar(string s, char c) {
    return s.Length - s.Replace(c.ToString(), "").Length;
  }
	public static void Main(){
      String[] temp=System.Console.ReadLine().Split(' ');
      int BurgerNum=int.Parse(temp[0]);
      int EatNum=int.Parse(temp[1]);
      String Burger="P";
      Burger=MakeBurger(BurgerNum,Burger);
      Burger=(Burger.Substring(Burger.Length-EatNum,EatNum));
      System.Console.WriteLine(CountChar(Burger, 'P'));
    }
}