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;

namespace abc115_d
{
    class Program
    {
        static void Main(string[] args)
        {
            long[] x = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long[] len = new long[x[0] + 1]; long[] p = new long[x[0] + 1];
            len[0] = 1; p[0] = 1;
            for (int i = 1; i <= x[0]; i++)
            {
                len[i] = len[i - 1] * 2 + 3;
                p[i] = p[i - 1] * 2 + 1;
            }
            long ret = 0; int now = (int)x[0]; bool middle = false;
            while (x[1] > 0)
            {
                if (middle)
                { x[1]--; ret++; middle = false; }
                else
                {
                    if (len[now] <= x[1])
                    {
                        x[1] -= len[now]; ret += p[now];
                        middle = true;
                    }
                    else { x[1]--; now--; }
                }
            }
            Console.WriteLine(ret);
        }
    }
}