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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class Main {
	
	 static long ans=0; 
	static long [] a=new long[52];
	static long [] b=new long[52];
    static void dfs(long p,int n)
     {
    //System.out.println(p+" "+n);
    //System.out.println(a[n-1]+" "+b[n-1]);
    	if(n==1) 
    	{
    		if(p==2)
    		{
    			ans+=1;
    		}
    		else if(p==3)
    		{
    			ans+=2;
    		}
    		else if(p==4)
    		{
    			ans+=3;
    		}
    	}
    	else
    	{
    		if(p==a[n-1]+2)
    		{
    			ans=ans+1+b[n-1];
    			return ;
    		}
    		else if(p==a[n])
    		{
    			ans=ans+b[n];
    			return;
    		}
    		else if(p==1)
    		{
    			return;
    		}
    		else if(p>a[n-1]+2)
    		{
    			ans=ans+b[n-1]+1;
    			dfs(p-a[n-1]-2,n-1);
    		}
    		else 
    		{
    			dfs(p-1,n-1);
    		}
    	}
    	return ;
     }
	public static void main(String args[])throws IOException  {

		Scanner in = new Scanner(System.in);
		
		int n=in.nextInt();
		long m=in.nextLong();
         
		a[1]=5;
		b[1]=3;
		for(int i=2;i<=n;i++)
		{
			a[i]=2*a[i-1]+3;
			b[i]=2*b[i-1]+1;
		}
		dfs(m,n);
		System.out.println(ans);
//		while(in.hasNext())
//		{
//			
//			
//		}
//
//			
//		}
//		
	}
	
}