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.Text;

namespace AtCoder
{
    internal static class Program
    {
        private static void Main()
        {
            long[] NX = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
            long N = NX[0];
            long X = NX[1];
            long res = 0;

            //lvl 0 = P = 0 buns
            //lvl 1 = BPPPB = 2 buns
            //lvl 2 = BBPPPBPBPPPBB = 6 buns 
            //lvl 3 = 14 buns
            //buns = (prevlevel * 2) + 2

            string burger = "";

            if (N == 0)
                if (X == 0)
                    res = 0;
                else
                    res = 1;
            else
            {
                string smallB = CreateBurger(N - 1);
                burger = "B" + smallB + "P" + smallB + "B";

                for (int i = 0; i < X; i++)
                    if (burger[i] == 'P')
                        res++;
            }

            Console.WriteLine(res);
        }

        private static string CreateBurger(long size) //100
        {
            StringBuilder b = new StringBuilder();
            
            if (size == 0)
                b.Append("P");
            else
            {
                string smallB = CreateBurger(size - 1);
                b.Append("B" + smallB + "P" + smallB + "B");
            }

            return b.ToString();
        }
    }
}