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;
using System.Collections.Generic;
using System.Linq;
class P{
  static void Main(){
   string[] s = Console.ReadLine().Split();
   int n = int.Parse(s[0]);
   int x = int.Parse(s[1]);
   string[] burger = new string[n + 1];
   burger[0] = "p";
   for (int i = 1; i <= n;i++){
     burger[i] = "b" + burger[i - 1] + "p";
      if (burger[i].Length > x){
       burger[i] = burger[i].Substring(0,x);
       continue;
      }
     burger[i] += burger[i - 1] + "b";
     if (burger[i].Length > x){
       burger[i] = burger[i].Substring(0,x);
       continue;
      }
   }
   long ans = 0;
   for (int i = 0;i < x;i++)
     ans += burger[n][i] == 'p' ? 1 : 0;
   Console.WriteLine(ans);
  }
}