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;
using static System.Console;
using System.Runtime.CompilerServices;
using static MyUtil;

class MyUtil
{
    public static long[] ReadLongArray()
    {
	return ReadLine().Split().Select(x => long.Parse(x)).ToArray();
    }
}

class Program
{
    static long[] a;
    static long[] p;

    public static void Main()
    {
	a = new long[51];
	p = new long[51];

	a[0] = p[0] = 1;
	for (int i = 1; i <= 50; i++)
	{
	    a[i] = a[i-1] * 2 + 3;
	    p[i] = p[i-1] * 2 + 1;
	}

	var tmp = ReadLongArray();
	int n = (int)tmp[0];
	long x = tmp[1];
	WriteLine(f(n, x));
    }

    static long f(int lv, long x)
    {
	if (lv == 0) return 1;
	
	if (x == 1)
	    return 0;
	else if (x < a[lv-1] + 2)
	    return f(lv - 1, x - 1);
	else if (x == a[lv-1] + 2)
	    return p[lv-1] + 1;
	else if (x < a[lv])
	    return p[lv-1] + 1 + f(lv - 1, x - a[lv-1] - 2);
	else
	    return p[lv-1] * 2 + 1;
    }
}