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.

Examples

Input

2 7


Output

4


Input

1 1


Output

0


Input

50 4321098765432109


Output

2160549382716056
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String[] nx = sc.nextLine().split(" ");
        int n = Integer.parseInt(nx[0]);
        long x = Long.parseLong(nx[1]);

        List<Long> burger = new ArrayList<>();
        List<Long> putty  = new ArrayList<>();
        burger.add(1L);
        putty.add(1L);
        for (int i = 0; i < n; i++) {
            burger.add(2 * burger.get(i) + 3);
            putty.add(2 * putty.get(i) + 1);
        }

        System.out.println(fnx(n, x, burger, putty));
    }

    public static long fnx(int n, long x, List<Long> a, List<Long> p) {
        if (n == 0) {
            return (x <= 0) ? 0 : 1;
        }
        if (x <= a.get(n - 1) + 1) {
            return fnx(n - 1, x - 1, a, p);
        }
        if (x == a.get(n - 1) + 2) {
            return p.get(n - 1) + 1;
        }
        if (a.get(n - 1) + 2 < x && x <= a.get(n) + 2) {
            return p.get(n - 1) + 1 + fnx(n - 1, x - 2 - a.get(n - 1), a, p);
        }
        return 2 * p.get(n - 1) + 1;
    }
}