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;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = ReadArrayLong();
            var N = input[0];
            var X = input[1];
            var sum = Psum(N) + Bsum(N);
            var chk = sum / 2 + 1;
            var ans = 0L;
            if (chk == X)
            {
                ans = Psum(N - 1) + 1;
                Console.WriteLine(ans);
                Console.ReadLine();
                return;
            }
            while (true)
            {
                if (N == 1)
                {
                    if (X == 2) ans += 1;
                    else if (X == 3) ans += 2;
                    else if (X >= 4) ans += 3;
                    break;
                }
                var P = Psum(N - 1);
                var B = Bsum(N - 1);                
                if (chk > X)
                {
                    X -= 1;
                    chk = P;
                    N--;
                }
                else if (chk < X)
                {
                    ans += P + 1;
                    X = X - (P + B + 2);
                    chk = P;
                    N--;
                }
                else
                {
                    ans += P + 1;
                    break;
                }
            }

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

        static long Psum(long num)
        {
            var ret = 1L;
            for (int i = 0; i < num; i++) ret = 2 * ret + 1;
            return ret;
        }

        static long Bsum(long num)
        {
            var ret = 0L;
            for (int i = 0; i < num; i++) ret = 2 * ret + 2;
            return ret;
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}