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: Accepted)

import java.util.*;

class Main{
	public static void main(String args[]) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		long x=sc.nextLong();
		long length[]=new long[n+1];
		long count=0;
		long pati[]=new long[n+1];
		//String s[]=new String[n+1];
		//s[0]="P";
		length[0]=1L;
		pati[0]=0L;
		for(int i=1;i<=n;++i) {
			//s[i]="B"+s[i-1]+"P"+s[i-1]+"B";
			length[i]=3+length[i-1]*2;
			pati[i]=1+2*pati[i-1];
		}
		
		//char c[]=s[n].toCharArray();
		int index=n;
		while(index>=0){
			if(x==1) {
				if(index==0)++count;
				break;
			}
			else if(x<=length[index]/2) {
				--index;
				--x;
			}
			else if(x==length[index]/2+1) {
				count=count+pati[index]+1;
				break;
			}
			else if(x==length[index]) {
				count = count+2*pati[index]+1;
				break;
			}
			else if(x>length[index]/2+1) {
				count =count+pati[index]+1;
				x=x-length[index]/2-1;
				--index;

			}

		}
		System.out.println(count);
	}
}