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 static Input;

public class Prog
{
    private const int INF = 1000000007;
    private static long[] data;
    private static long[] Pdata;
    public struct Pair<T> { public T x, y; public Pair(T x, T y) { this.x = x; this.y = y; } }
    public static void Solve()
    {
        int N = NextInt();
        long X = NextLong();
        data = new long[60];
        Pdata = new long[60];
        data[0] = 1;
        Pdata[0] = 1;
        for (int i = 0; i <= 50; i++)
        {
            data[i + 1] = data[i] * 2 + 3;
            Pdata[i + 1] = Pdata[i] * 2 + 1;
        }
        Console.WriteLine(Christmas(N, X));
    }
    public static long Christmas(long n, long x)
    {
        //レベル0バーガーはパティなので
        if (n == 0) return 1;
        //前のレベルバーガーを計算
        long h = data[n - 1];
        long p = Pdata[n - 1];
        //Bしか食べれない
        if (x == 1) return 0;
        //前のレベルの半分も食べれない
        else if (x <= h + 1) return Christmas(n - 1, x - 1);
        //ちょうど半分
        else if (x == h + 2) return p + 1;
        //半分以上食べれる
        else if (x <= h * 2 + 2) return p + 1 + Christmas(n - 1, x - h - 2);
        //全部食べる
        else return 2 * p + 1;
    }
    public static void Main()
    {
        var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
    }
}

public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static char NextChar() { Confirm(); return char.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}