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: Runtime Error)

import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int x = sc.nextInt();
    int[] f = new int[n + 1];
    f[0] = 1;
    for(int i = 1; i <= n; i++) {
      f[i] = 2 * f[i - 1] + 3;
    }
    int[][] dp = new int[n + 1][f[n] + 1];
    dp[0][1] = 1;
    for(int i = 1; i <= n; i++) {
      for(int j = 2; j <= f[i]; j++) {
        if(j <= (1 + f[i - 1])) {
          dp[i][j] = dp[i - 1][j - 1];
        } else if(j == (2 + f[i - 1])) {
          dp[i][j] = dp[i - 1][f[i - 1]] + 1;
        } else if(j < f[i]) {
          dp[i][j] = dp[i - 1][f[i - 1]] + 1 + dp[i - 1][j - 2 - f[i - 1]];
        } else {
          dp[i][j] = 2 * dp[i - 1][f[i - 1]] + 1; 
        }
      }
    }
    System.out.println(dp[n][x]);
  }
}