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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static long[] levelNum = new long[51];
        static long[] pattyNum = new long[51];
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var NX = Sarray();
            var N = NX[0];
            var X = NX[1];
            levelNum[0] = 1;
            pattyNum[0] = 1;
            for (var i = 1; i <= N; ++i)
            {
                levelNum[i] = 3 + 2 * levelNum[i - 1];
                pattyNum[i] = 1 + 2 * pattyNum[i - 1];
            }
            var ans = lunlun(N, X);
            WriteLine(ans);
            //Out.Flush();
        }
        static long lunlun(long layer, long x)
        {
            //B L[i-1] P L[i-1] B
            var patty = 0L;
            --x;
            if (levelNum[layer - 1] <= x) patty += pattyNum[layer - 1];
            else if (0 < x) patty += lunlun(layer - 1, x);
            x -= levelNum[layer - 1];
            if (0 < x) ++patty;
            --x;
            if (levelNum[layer - 1] <= x) patty += pattyNum[layer - 1];
            else if (0 < x) patty += lunlun(layer - 1, x);
            return patty;
        }
    }
}