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: Time Limit Exceeded)

import java.util.*;

class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String[] line = scanner.nextLine().split(" ", 2);
        long n = Long.parseLong(line[0]);
        long x = Long.parseLong(line[1]);
        new Main(x, 0).main(n);
    }

    private long toEat;
    private long pati;

    public Main(long toEat, long pati) {
        this.toEat = toEat;
        this.pati = pati;
    }

    public void main(long level) {
        this.eat(level);
        System.out.println(this.pati);
    }

    public void eat(long level) {
        if (toEat == 0) {
            return;
        }

        if (level == 0) {
            this.toEat--;
            this.pati++;
        } else {
            this.toEat--; // ban

            if (this.toEat > 0) { // level - 1 burger
                this.eat(level - 1);
            }
            if (this.toEat > 0) { // pati
                this.toEat--;
                this.pati++;
            }
            if (this.toEat > 0) { // level - 1 burger
                this.eat(level - 1);
            }
            if (this.toEat > 0) { // ban
                this.toEat--;
            }
        }
    }
}