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: Accepted)

#if DEBUG
using Microsoft.VisualStudio.TestTools.UnitTesting;
#endif
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Contest
{
    class Program
    {
        public static IO.StreamScanner scanner = new IO.StreamScanner(Console.OpenStandardInput());

        static void Main(string[] args)
        {
            var n = scanner.Integer();
            var x = scanner.Long();

            var ans = GetAns(n, (ulong)x);

            IO.Printer.Out.WriteLine(ans);
            IO.Printer.Out.Flush();
        }

        public static ulong GetAns(int n, ulong x)
        {
            var layers = GetLayers(n);
            return Dp(n, x, layers);
        }

        static Dictionary<Tuple<int, ulong>, ulong> _memo = new Dictionary<Tuple<int, ulong>, ulong>();

        public static ulong Dp(int l, ulong d, ulong[] layers)
        {
            if (l < 0 || d <= 0) return 0L;
            if (l == 0 && d >= 1) return 1L;

            var key = new Tuple<int, ulong>(l, d);
            if (_memo.ContainsKey(key)) return _memo[key];

            var ret = 0uL;

            var n = layers[l];

            if (d >= n / 2 + 1)
            {
                ret = 1 + Dp(l - 1, layers[l - 1], layers) + Dp(l - 1, d - 2 - layers[l - 1], layers);
            }
            else
            {
                ret = Dp(l - 1, d - 1, layers);
            }

            _memo[key] = ret;
            return ret;
        }

        public static ulong[] GetLayers(int n)
        {
            var ret = new ulong[n + 1];
            ret[0] = 1;
            for (int i = 1; i <= n; i++)
            {
                ret[i] = 3 + 2 * ret[i - 1];
            }
            return ret;
        }
    }

#if DEBUG
    [TestClass]
    public class Test
    {
        [TestMethod]
        public void Test1()
        {
            var n = 2;
            var x = 7ul;
            var exp = 4ul;
            var ans = Program.GetAns(n, x);
            Assert.AreEqual(exp, ans);
        }

        [TestMethod]
        public void Test2()
        {
            var n = 1;
            var x = 1ul;
            var exp = 0ul;
            var ans = Program.GetAns(n, x);
            Assert.AreEqual(exp, ans);
        }

        [TestMethod]
        public void Test3()
        {
            var n = 50;
            var x = 4321098765432109ul;
            var exp = 2160549382716056ul;
            var ans = Program.GetAns(n, x);
            Assert.AreEqual(exp, ans);
        }


        bool IsEq(IEnumerable<char> l1, IEnumerable<char> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i > l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        bool IsEq(IEnumerable<int> l1, IEnumerable<int> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for(int i=0; i>l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        bool IsEq(IEnumerable<long> l1, IEnumerable<long> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i > l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        bool IsEq(IEnumerable<double> l1, IEnumerable<double> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i > l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        bool IsEq(double d1, double d2)
        {
            return Math.Abs(d2 - d1) < 1E10;
        }

    }
#endif

    namespace IO
    {
        using System.IO;
        using System.Text;
        using System.Globalization;

        public class Printer : StreamWriter
        {
            static Printer()
            {
                Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false };
            }

            public static Printer Out { get; set; }

            public override IFormatProvider FormatProvider
            {
                get { return CultureInfo.InvariantCulture; }
            }

            public Printer(Stream stream)
                : base(stream, new UTF8Encoding(false, true))
            {
            }

            public Printer(Stream stream, Encoding encoding)
                : base(stream, encoding)
            {
            }

            public void Write<T>(string format, T[] source)
            {
                base.Write(format, source.OfType<object>().ToArray());
            }

            public void WriteLine<T>(string format, T[] source)
            {
                base.WriteLine(format, source.OfType<object>().ToArray());
            }
        }

        public class StreamScanner
        {
            public StreamScanner(Stream stream)
            {
                str = stream;
            }

            public readonly Stream str;
            private readonly byte[] buf = new byte[1024];
            private int len, ptr;
            public bool isEof;

            public bool IsEndOfStream
            {
                get { return isEof; }
            }

            private byte read()
            {
                if (isEof) return 0;
                if (ptr < len) return buf[ptr++];
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
                isEof = true;
                return 0;
            }

            public char Char()
            {
                byte b;
                do b = read(); while ((b < 33 || 126 < b) && !isEof);
                return (char)b;
            }

            public string Scan()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                    sb.Append(b);
                return sb.ToString();
            }

            public string ScanLine()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b != '\n'; b = (char)read())
                    if (b == 0) break;
                    else if (b != '\r') sb.Append(b);
                return sb.ToString();
            }

            public long Long()
            {
                if (isEof) return long.MinValue;
                long ret = 0;
                byte b;
                var ng = false;
                do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
                if (b == 0) return long.MinValue;
                if (b == '-')
                {
                    ng = true;
                    b = read();
                }
                for (; ; b = read())
                {
                    if (b < '0' || '9' < b)
                        return ng ? -ret : ret;
                    ret = ret * 10 + b - '0';
                }
            }

            public int Integer()
            {
                return (isEof) ? int.MinValue : (int)Long();
            }

            public double Double()
            {
                var s = Scan();
                return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
            }

            static T[] enumerate<T>(int n, Func<T> f)
            {
                var a = new T[n];
                for (int i = 0; i < n; ++i) a[i] = f();
                return a;
            }

            public char[] Char(int n)
            {
                return enumerate(n, Char);
            }

            public string[] Scan(int n)
            {
                return enumerate(n, Scan);
            }

            public double[] Double(int n)
            {
                return enumerate(n, Double);
            }

            public int[] Integer(int n)
            {
                return enumerate(n, Integer);
            }

            public long[] Long(int n)
            {
                return enumerate(n, Long);
            }
        }
    }
}