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: Wrong Answer)

using System;

class Program
{
    //Level k の時のpの数を格納
    static readonly long[] dp = new long[51];
    static readonly long[] lengthDp = new long[51];

    static void SetDP(int n, int i)
    {
        dp[i] = dp[i - 1] * 2 + 1;
        lengthDp[i] = lengthDp[i - 1] * 2 + 3;
        i++;
        if (i <= n) SetDP(n, i);
    }

    static long GetRightPCount(int n, long x, int originalN)
    {
        long count = 0;

        //n個のB/set[i-1](先頭のBを除く)/P/set[i-1]/ /終端のn-i+1個のB
        //n個のB
        if (x <= n) return count;
        x -= n;

        //set[i-1](先頭のBは除く)
        int i;
        for (i = 0; i < n; i++)
            if (x < lengthDp[i])
                break;
        if (i == 0) return count;
        count += dp[i - 1];
        x -= lengthDp[i - 1] - i + 1;
        if (x <= 0) return count;

        //P
        count++;
        x--;

        if (x <= originalN- i + 1) return count;
        
        return count + GetRightPCount(i - 1, x, originalN);
    }

    static void Main(string[] args)
    {
        string[] input = Console.ReadLine().Split(' ');
        int n = int.Parse(input[0]);
        long x = long.Parse(input[1]);

        dp[0] = 1;
        lengthDp[0] = 1;
        SetDP(n, 1);

        Console.WriteLine(GetRightPCount(n, x, n));
    }
}