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;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		long[] P = new long[N + 1];
		long[] B = new long[N + 1];
		P[0] = 1;
		B[0] = 0;
		for(int i=1;i<=N;i++){
			P[i] = P[i-1] * 2 + 1;
			B[i] = B[i-1] * 2 + 2;
		}
		
		long ans = 0;
		for(int i=N;i>0;i--){
			if(X == 0) break;
			long tot = B[i] + P[i];
			if(X == tot){
				ans += P[i];
				X -= tot;
				break;
			}
			
			if(X >= (B[i-1] + P[i-1]) * 2 + 2){
				ans += P[i-1] * 2 + 1;
				X -= (P[i-1] + B[i-1]) * 2 + 2 + 1;
				continue;
			}
			if(X > (B[i-1] + P[i-1]) + 2){
				ans += P[i - 1] + 1;
				X -= (P[i - 1] + B[i - 1] + 2);
				continue;
			}
			
			if(X == (B[i-1] + P[i-1]) + 2){
				ans += P[i - 1] + 1;
				X -= (B[i-1] + P[i-1]) + 2;
				continue;
			}
			X -= 1;
		}
		Console.WriteLine(ans);
	}
	int N;
	long X;
	public Sol(){
		var d = rla();
		N = (int)d[0]; X = d[1];
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}