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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ABC115_D solver = new ABC115_D();
        solver.solve(1, in, out);
        out.close();
    }

    static class ABC115_D {
        static private long[] paties = new long[51];
        static private long[] height = new long[51];

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            long x = in.nextLong();
            paties(n, paties);
            height(n, height);
            long ans = answer(n, x);

            out.print(ans);


        }

        private long answer(int n, long x) {
            if (n == 0) {
                if (x <= 0) {
                    return 0;
                } else {
                    return 1;
                }
            }

            if (x <= 1 + height[n - 1]) {
                return answer(n - 1, x - 1);
            } else {
                return paties[n - 1] + 1 + answer(n - 1, x - 2 - height[n - 1]);
            }
        }

        private long paties(int n, long[] paties) {
            if (n == 0) {
                paties[n] = 1;
                return 1;
            } else {
                long p = paties(n - 1, paties);
                paties[n] = 2 * p + 1;
                return 2 * p + 1;
            }
        }

        private long height(int n, long[] height) {
            if (n == 0) {
                height[n] = 1;
                return 1;
            } else {
                long h = height(n - 1, height);
                height[n] = 2 * h + 3;
                return 2 * h + 3;
            }

        }

    }
}