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;

class test
{
    static List<int> CB(int N) {
        if(N == 0) return new List<int>(){1};
        List<int> Result = new List<int>();
        List<int> monB = CB(N - 1);
        Result.Add(0);
        foreach(int e in monB) Result.Add(e);
        Result.Add(1);
        foreach(int e in monB) Result.Add(e);
        Result.Add(0);

        return Result;
    }
    static void Main(){
        //パティ - 1
        //パン - 0
        string[] Inputs = Console.ReadLine().Split(' ');
        int N = Int32.Parse(Inputs[0]);
        int X = Int32.Parse(Inputs[1]);
        List<int> B = CB(N);

        int Result = 0;
        for(int count = B.Count -1;B.Count - count< X;count--)
            Result += B[count];

        Console.WriteLine(Result);
    }
}