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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Diagnostics.CodeAnalysis;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Runtime.Remoting;
using System.Runtime.Remoting.Contexts;
using System.Text;
using System.Threading;
using System.Xml.Schema;

namespace Contest
{
    class Scanner
    {
        private string[] line = new string[0];
        private int index = 0;

        public string Next()
        {
            if (line.Length <= index)
            {
                line = Console.ReadLine().Split(' ');
                index = 0;
            }

            var res = line[index];
            index++;
            return res;
        }

        public int NextInt()
        {
            return int.Parse(Next());
        }

        public long NextLong()
        {
            return long.Parse(Next());
        }

        public ulong NextUlong()
        {
            return ulong.Parse(Next());
        }

        public string[] Array()
        {
            line = Console.ReadLine().Split(' ');
            index = line.Length;
            return line;
        }

        public int[] IntArray()
        {
            var array = Array();
            var result = new int[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = int.Parse(array[i]);
            }

            return result;
        }

        public long[] LongArray()
        {
            var array = Array();
            var result = new long[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = long.Parse(array[i]);
            }

            return result;
        }
    }

    class Program
    {
        private int N;
        private long X;
        private long[] Size;
        private long[] PP;
        private void Scan()
        {
            var sc = new Scanner();
            N = sc.NextInt();
            X = sc.NextLong();
        }

        public void Solve()
        {
            Scan();
            Size = new long[51];
            PP = new long[51];
            Size[0] = 1;
            PP[0] = 1;
            for (int i = 1; i <= 50; i++)
            {
                Size[i] = Size[i - 1] * 2 + 3;
                PP[i] = PP[i - 1] * 2 + 1;
            }
            Console.WriteLine(EatP(N, X));
        }

        private long EatP(int l, long n)
        {
            if (l == 0)
            {
                if (n == 1)
                {
                    return 1;
                }
                else
                {
                    return 0;
                }
            }

            long result = 0;

            if (n <= 1)
            {
                return 0;
            }

            if (n > 1 && n <= 1 + Size[l - 1])
            {
                return EatP(l - 1, n - 1);
            }

            if (n == Size[l - 1] + 2)
            {
                return EatP(l - 1, n - 1) + 1;
            }

            if (n > Size[l - 1] + 2 && n <= Size[l - 1] * 2 + 2)
            {
                return PP[l - 1] + 1 + EatP(l - 1, n - Size[l - 1] - 1);
            }

            return PP[l];
        }

        static void Main() => new Program().Solve();
    }


}