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;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace D
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var nx = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
            var n = (int)nx[0];
            var pi = new long[n];
            pi[0] = 1;
            var ai = new long[n];
            ai[0] = 1;
            for (var i = 1; i < nx[0]; i++)
            {
                pi[i] = pi[i - 1] * 2 + 1;
                ai[i] = ai[i - 1] * 2 + 3;
            }
            Console.WriteLine(F(ai, pi, n, nx[1]));
        }

        static long F(long[] all, long[] patties, int n, long x)
        {
            if (n == 0) return x <= 0 ? 0 : 1;
            else if (x <= 1 + all[n - 1]) return F(all, patties, n - 1, x - 1);
            else return patties[n - 1] + 1 + F(all, patties, n - 1, x - 2 - all[n - 1]);
        }
    }
}