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.*;
import java.lang.*;


public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long x = sc.nextLong();
        long eatp = 0;
        long eati = n;
        boolean th = false;
        for (long i = n; i > 0; i--) {
            if ((eati - i) + Math.pow(2, i + 2) - 3 <= x) {
                th = true;
                eatp += Math.pow(2, i + 1) - 1;
                x -= (eati - i) + Math.pow(2, i + 2) - 3;
                eati = i;
                if (x == 0) {
                    break;
                } else {
                    x--;
                    eatp++;
                }
            }
        }
        if (!th) {
            x--;
        } else {
            x -= eati - 1;
        }
        if (x == 2) {
            eatp++;
        } else if (x == 3) {
            eatp += 2;
        } else if (x >= 4) {
            eatp += 3;
        }
        System.out.println(eatp);
    }
}