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.Text;

namespace AtTest.ABC_115
{
    class D
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            long[] nx = ReadLongs();
            long n = nx[0];
            long x = nx[1];
            var pCnt = new long[n+1][];// all, p  L= 0 ~ n
            pCnt[0] = new long[2] { 1, 1 };
            for(int i = 1; i <= n; i++)
            {
                pCnt[i] = new long[2] {
                    pCnt[i-1][0] * 2 + 3, pCnt[i - 1][1] * 2 + 1 };
            }
            long cnt = 0;
            long nn = n;
            long now = x - 1;
            while (nn > 0)
            {
                if (now == 0)
                {
                    Console.WriteLine(cnt);
                    return;
                }
                else if (now < pCnt[nn][0] / 2)
                {
                    now--;
                    nn--;
                }
                else if(now==pCnt[nn][0]/2)
                {
                    Console.WriteLine(cnt + pCnt[nn - 1][1] + 1);
                    return;
                }
                else if (now < pCnt[nn][0]-1)
                {
                    now -= pCnt[nn - 1][0] + 2;
                    cnt += pCnt[nn - 1][1] + 1;
                    nn--;
                }
                else if (now == pCnt[nn][0]-1)
                {
                    Console.WriteLine(cnt + pCnt[nn][1]);
                    return;
                }

            }
            Console.WriteLine(cnt + 1);
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}