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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Collections;
using System.Threading.Tasks;
using System.Threading;

namespace testing
{
    class Program
    {
        static void Main(string[] args)
        {
            int N, X, a;
            int ans = 0;
            a = int.Parse(Console.ReadLine()); //標準入力
            string[] str = Console.ReadLine().Split(' ');//2つ以上のスペース区切り入力の取得
            N = int.Parse(str[0]);  //数値で受け取りたい場合は変換する
            X = int.Parse(str[1]);

            var bg = new List<string> { "P" };
            List<string> bg_cp;

            for (int i = 0; i < N; i++)
            {
                bg_cp = new List<string>(bg);
                bg.Insert(0, "B");
                bg.Add("P" + bg_cp + "B");
            }

            for (int i = 0; i < X; i++)
            {
                if (bg[i] == "P")
                {
                    ans++;
                }
            }

            Console.WriteLine(ans);
            Console.ReadKey();
        }
    }
}