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[] AtsusaDP = new long[51];

    static {
        AtsusaDP[0] = 1L;
        for (int i = 0; i < 50; i++) {
            AtsusaDP[i + 1] = 3L + 2 * AtsusaDP[i];
        }
    }

    public static long[] P_CountDP = new long[51];

    static {
        P_CountDP[0] = 1;
        for (int i = 0; i < 50; i++) {
            P_CountDP[i + 1] = 1L + 2 * P_CountDP[i];
        }
    }


    public static long ans = 0L;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long x = sc.nextLong();

        eatBG(n, x);
        System.out.println(ans);
    }

    /**
     * @param level ハンバーガーのレベル
     * @param rest  残りの食べるべき数
     * @return 新しい残りの食べるべき数
     */
    private static long eatBG(int level, long rest) {
        if (level == 0) {
            if (rest > 0) {//P part
                ans++;
                return rest--;
            } else {
                return rest;
            }
        }

        if (rest >= AtsusaDP[level]) {
            rest -= AtsusaDP[level];
            ans += P_CountDP[level];
            return rest;
        } else {
            rest--;//B part
            if (rest > 0) rest = eatBG(level - 1, rest);// n-1 BG part
            if (rest > 0) {//P part
                rest--;
                ans++;
            }
            if (rest > 0) {//n-1 part
                rest = eatBG(level - 1, rest);
            }
            rest--;//B part
            return rest;
        }
    }
}