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.*;

public class Main {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long x = sc.nextLong();
		Bargar b = new Bargar(n);
		System.out.println(b.getAmount(x));
    }
    
    static class Bargar {
        int size;
        long count;
        long paties;
        
        Bargar inside;
        
        public Bargar (int size) {
            this.size = size;
            if (size == 0) {
                count = 1;
                paties = 1;
            } else {
                inside = new Bargar(size - 1);
                count = inside.count * 2 + 3;
                paties = inside.paties * 2 + 1;
            }
        }
        
        public long getAmount(long total) {
            if (size == 0) {
                return 1;
            }
            long ans = 0;
            total--;
            if (total <= 0) {
                return ans;
            }
            if (total <= inside.count) {
                return inside.getAmount(total);
            }
            ans += inside.paties;
            total -= inside.count;
            if (total <= 0) {
                return ans;
            }
            total--;
            ans++;
            if (total <= 0) {
                return ans;
            }
            return ans + inside.getAmount(total);
        }
    }
}