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 D
{
    public class Program

    {

        static long[] burgerCnt;
        static long[] pattyCnt;

        public static void Main(string[] args)
        {
            long[] line = ReadLongAr();
            long n = line[0];
            long x = line[1];

            burgerCnt = new long[n + 1];
            pattyCnt = new long[n + 1];

            for (int i = 0 ; i <= n ; i++)
            {
                if (i == 0)
                {
                    burgerCnt[i] = 1;
                    pattyCnt[i] = 1;
                }
                else
                {
                    burgerCnt[i] = burgerCnt[i - 1] * 2 + 3;
                    pattyCnt[i] = pattyCnt[i - 1] * 2 + 1;
                }
            }

            long res = CountPatty(n, x);
            Console.WriteLine(res.ToString());

        }

        private static long CountPatty(long n, long x)
        {
            if (n == 0) return 1;
            if (x == 1) return 0;
            if (1 < x && x <= 1 + burgerCnt[n - 1]) return CountPatty(n - 1, x - 1);
            if (1 + burgerCnt[n - 1] < x && x <= 1 + burgerCnt[n - 1] + 1) return pattyCnt[n - 1] + 1;
            if (1 + burgerCnt[n - 1] + 1 < x && x <= burgerCnt[n] - 1) return pattyCnt[n - 1] + 1 + CountPatty(n - 1, x - (1 + burgerCnt[n - 1] + 1));
            if (x == burgerCnt[n]) return pattyCnt[n];
            return 0;
        }

        static string ReadSt() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Console.ReadLine()); }
        static long ReadLong() { return long.Parse(Console.ReadLine()); }
        static double ReadDouble() { return double.Parse(Console.ReadLine()); }
        static string[] ReadStAr(char sep = ' ') { return Console.ReadLine().Split(sep); }
        static int[] ReadIntAr(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Split(sep), e => int.Parse(e)); }
        static long[] ReadLongAr(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Split(sep), e => long.Parse(e)); }
        static double[] ReadDoubleAr(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Split(sep), e => double.Parse(e)); }

    }

}