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;
using System.Threading.Tasks;

class P
{
    static long[] padCount = new long[51];
    static long[] totalCount = new long[51];
    static void Main()
    {
        padCount[0] = 1;
        totalCount[0] = 1;
        for (int i = 1; i < 51; i++)
        {
            padCount[i] = padCount[i - 1] * 2 + 1;
            totalCount[i] = totalCount[i - 1] * 2 + 3;
        }
        long[] nx = Console.ReadLine().Split().Select(long.Parse).ToArray();

        Console.WriteLine(Solve((int)nx[0], nx[1]));
    }

    static long Solve (int n, long x)
    {
        if (x == 0) return 0;
        if(n == 0) return 1;
        x--;
        if (x == 0) return 0;
        if (x <= totalCount[n - 1]) return Solve(n - 1, x);
        x -= totalCount[n - 1];
        if (x == 0) return padCount[n - 1];
        x--;
        if (x == 0) return padCount[n - 1] + 1;
        if (x <= totalCount[n - 1]) return padCount[n - 1] + 1 + Solve(n - 1, x);
        return padCount[n];
    }

}