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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Net.Sockets;
using static System.Console;

class Program
{
    static void Main(string[] args)
    {
        var NX = ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
        var (N, X) = (NX[0], NX[1]);

        var pCount = new long[51];
        var pbLength = new long[51];
        pCount[0] = 1;
        pbLength[0] = 1;
        for (int i = 1; i <= 50; i++)
        {
            pCount[i] = pCount[i - 1] * 2 + 1;
            pbLength[i] = pbLength[i - 1] * 2 + 3;
        }

        long func(long n, long x)
        {
            if(x < pbLength[n])
            {
                var a = 0L;

                x--;
                if (x <= 0)
                    return a;
                
                a += func(n - 1, x);
                x -= pbLength[n - 1];
                if (x <= 0)
                    return a;
                
                a++;
                x--;
                if (x <= 0)
                    return a;

                a += func(n - 1, x);

                return a;
            }
            else
            {
                return pCount[n];
            }
        }

        var ans = func(N, X);

        WriteLine(ans);
    }
}