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.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;

class Program
{
    const string Yes = "Yes";
    const string No = "No";
    const long Mod = 1000000007;

    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static List<long> lvlpaty = new List<long>();
    static List<long> lvlsou = new List<long>();

    static object process(TextReader input) {
        var spl = input.ReadLine().Split(' ');
        var n = int.Parse(spl[0]);
        var x = long.Parse(spl[1]);

        lvlpaty.Clear();
        lvlsou.Clear();

        lvlpaty.Add(1);
        lvlsou.Add(1);

        for (int i = 1; i <= n; i++) {
            lvlpaty.Add(1 + lvlpaty[i - 1] * 2);
            lvlsou.Add(3 + lvlsou[i - 1] * 2);
        }

        return patiy(n, ref x);
    }

    static long patiy(int level, ref long x) {
        if(lvlsou[level] <= x) {
            x -= lvlsou[level];
            return lvlpaty[level];
        }
        if(level == 0) {
            x--;
            return 1;
        }

        long r = 0;

        x--;
        if (x == 0) return r;

        r += patiy(level - 1,ref x);
        if (x == 0) return r;

        r++; x--;
        if (x == 0) return r;

        r += patiy(level - 1, ref x);
        if (x == 0) return r;

        x--;
        return r;
    }
}