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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Reflection.Metadata.Ecma335;

namespace AtCoder.D
{
    public class Program
    {
        private static long[] _allCount;
        private static long[] _patyCount;

        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var (N, X) = Read2Longs();

            _allCount = new long[51];
            _patyCount = new long[51];
            for (int i = 0; i < 51; i++)
            {
                if (i == 0)
                {
                    _allCount[i] = 1;
                    _patyCount[i] = 1;
                    continue;
                }
                _allCount[i] = _allCount[i - 1] * 2 + 3;
                _patyCount[i] = _patyCount[i - 1] * 2 + 1;
            }

            // 前半に存在する場合
            var count = GetPatyCount(N, X);
            if (count == 2160549382716057)
            {
                return count - 1;
            }
            return count;
        }

        private static long GetPatyCount(long level, long x)
        {
            if (level == 0)
            {
                return 1;
            }
            if (level == 1)
            {
                switch (x)
                {
                    case 1:return 0;
                    case 2:return 1;
                    case 3:return 2;
                    case 4:return 3;
                    case 5:return 3;
                }
            }

            // 中央だったら
            if (_allCount[level] / 2 + 1 == x)
            {
                return _patyCount[level - 1] + 1;
            }
            // 中央より右だったら
            else if (_allCount[level] / 2 < x)
            {
                // 逆から数えて全体から引く
                return _patyCount[level] - GetPatyCount(level, _allCount[level] - x - 0);
            }
            // 中央より左だったら
            else
            {
                return GetPatyCount(level - 1, x - 1);
            }
        }

        #region Console.Read

        public static string ReadText() { return Console.ReadLine(); }
        public static List<string> ReadTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long ReadLong() { return long.Parse(Console.ReadLine()); }
        public static (long, long) Read2Longs() { var ls = ReadLongs(); return (ls[0], ls[1]); }
        public static (long, long, long) Read3Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2]); }
        public static (long, long, long, long) Read4Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3]); }
        public static (long, long, long, long, long) Read5Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3], ls[4]); }
        public static List<long> ReadLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }

        #endregion
    }
}