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;

namespace AtCoder.D
{
    public class Program
    {
        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var (N, X) = Read2Longs();
            var p = new long[N + 1];
            var count = new long[N + 1];
            count[0] = 1;
            p[0] = 1;
            for (var i = 1; i <= N; i++)
            {
                count[i] = 2 * count[i - 1] + 3;
                p[i] = 2 * p[i - 1] + 1;
            }
            var pcount = 0L;
            var j = N;
            while (X > 0 && j > 0)
            {
                var kukaku = GetKukaku(count[j], X);
                if (kukaku == 1)
                {
                    X--;
                }
                else if (kukaku == 2)
                {
                    X -= 1;
                }
                else if (kukaku == 3)
                {
                    pcount += p[j - 1] + 1;
                    X -= X;
                }
                else if (kukaku == 4)
                {
                    pcount += p[j - 1] + 1;
                    X -= count[j - 1] + 2;
                }
                else if (kukaku == 5)
                {
                    pcount += p[j];
                    X -= X;
                }
                j--;
            }
            return pcount;
        }
        private static int GetKukaku(long n, long x)
        {
            var line = (n - 3) / 2;
            if (x == 1)
            {
                return 1;
            }
            else if (x <= line + 1)
            {
                return 2;
            }
            else if (x == line + 2)
            {
                return 3;
            }
            else if (x <= 2 * line + 2)
            {
                return 4;
            }
            else
            {
                return 5;
            }
        }
        #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
    }
}