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)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCoder
{
    class Solver
    {
        private readonly long[] L;
        private Dictionary<Tuple<int, long>, long> memo;
        public Solver()
        {
            L = new long[51];
            L[0] = 1;
            for (int i = 1; i <= 50; ++i) { L[i] = L[i - 1] * 2 + 3; }
            memo = new Dictionary<Tuple<int, long>, long>();
        }
        public long Solve(int N, long X)
        {
            if (X <= 0) { return 0; }
            if (N == 0) { return 1; }
            var key = new Tuple<int, long>(N, X);
            if (!memo.ContainsKey(key))
            {
                long sum = 0;
                long M = L[N - 1];
                if (X - 1 > 0)     { sum += Solve(N - 1, Math.Min(X - 1, M)); }
                if (X - M - 1 > 0) { sum += 1; }
                if (X - M - 2 > 0) { sum += Solve(N - 1, Math.Min(X - M - 2, M)); }
                memo[key] = sum;
            }
            return memo[key];
        }
    }
    class Program
    {
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }

        static void Main(string[] args)
        {
            long[] V = ReadLongs();
            Console.WriteLine(new Solver().Solve((int)V[0], V[1]));
        }
    }
}