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.util.Scanner;

public class Main {

  public static long heightOfBurger(int level) {
    if (level == 0) {
      return 1;
    } else {
      return heightOfBurger(level - 1) * 2 + 3;
    }
  }

  public static long numberOfPatty(int level) {
    if (level == 0) {
      return 1;
    } else {
      return numberOfPatty(level - 1) * 2 + 1;
    }
  }

  public static long answer(int level, long layer) {
    if (layer == 1) {
      return 0;
    } else if (layer <= heightOfBurger(level - 1) + 1) {
      return answer(level - 1, layer - 1);
    } else if (layer == heightOfBurger(level - 1) + 2) {
      return numberOfPatty(level - 1) + 1;
    } else if (layer <= heightOfBurger(level) - 1) {
      return numberOfPatty(level - 1) + 1 + answer(level - 1, layer - heightOfBurger(level - 1) - 2);
    } else {
      return numberOfPatty(level);
    }
  }

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int level = sc.nextInt();
    long layer = sc.nextLong();
    System.out.println(answer(level, layer));
  }
}