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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        long X = scan.nextLong();
        // level 0 P
        // level 1 BPPPB
        // level 2 BBPPPBPBPPPBB
        long answer = count_pan(N, X);
        System.out.println(answer);
    }
    private long pan(int N) {
        long pan = 1;
        for (int i = 1; i <= N; i++) {
            pan = pan * 2 + 1;
        }
        return pan;
    }
    private long len(int N) {
        long len = 1;
        for (int i = 1; i <= N; i++) {
            len = len * 2 + 3;
        }
        return len;
    }
    private long count_pan(int N, long K) {
        if (N == 0) {
            return 1;
        }
        if (K == 1) {
            return 0;
        }
        long len = len(N);
        if (K == len) {
            return pan(N);
        }
        if (K == len/2 + 1) {
            return pan(N-1) + 1;
        }
        if (len/2 + 1 < K) {
            return pan(N-1) + count_pan(N-1, K - len/2 - 1) + 1;
        }
        return count_pan(N-1, K - 1);
    }
}