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;

namespace ABC115_D___Christmas
{
    class Program
    {
        static long[] burger;
        static long[] patty;
        static void Main(string[] args)
        {
            var NX = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
            var N = NX[0];
            var X = NX[1];

            burger = new long[N + 1];
            burger[0] = 1;
            for (int i = 1; i < N + 1; i++) burger[i] = burger[i - 1] * 2 + 3;

            patty = new long[N + 1];
            patty[0] = 1;
            for (int i = 1; i < N + 1; i++) patty[i] = patty[i - 1] * 2 + 1;

            Console.WriteLine(Eat(N, X));
        }

        static long Eat(long N, long X)
        {
            if (N == 0) return X == 1 ? 1 : 0;
            if (X <= burger[N - 1] + 1) return Eat(N - 1, X - 1);
            if (X == burger[N]) return patty[N];
            return 1 + patty[N - 1] + Eat(N - 1, X - 2 - burger[N - 1]);
        }
    }
}