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.util.*;
import java.io.*;

public class Main {

  private static void solve() {
    int n = nextInt();
    long x = nextLong();

    long[] l = new long[n + 1];
    long[] p = new long[n + 1];

    l[0] = 1;
    p[0] = 1;
    for (int i = 1; i <= n; i++) {
      l[i] = 2 * l[i - 1] + 3;
      p[i] = 2 * p[i - 1] + 1;
    }

    System.out.println(get(n, x, l, p));
  }

  private static long get(int n, long x, long[] l, long[] p) {
    if (n == 0) {
      return 1;
    }

    if (x == 1) {
      return 0;
    }

    x--;

    if (x <= l[n - 1]) {
      return get(n - 1, x, l, p);
    }

    x -= l[n - 1];

    if (x == 1) {
      return p[n - 1] + 1;
    }

    x--;

    if (x == l[n - 1] + 1) {
      x--;
    }
    
    return p[n - 1] + 1 + get(n - 1, x, l, p);
  }

  private static void run() {
    br = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out);

    solve();

    out.close();
  }

  private static StringTokenizer st;
  private static BufferedReader br;
  private static PrintWriter out;

  private static String next() {
    while (st == null || !st.hasMoreElements()) {
      String s;
      try {
        s = br.readLine();
      } catch (IOException e) {
        return null;
      }
      st = new StringTokenizer(s);
    }
    return st.nextToken();
  }

  private static int nextInt() {
    return Integer.parseInt(next());
  }

  private static long nextLong() {
    return Long.parseLong(next());
  }

  public static void main(String[] args) {
    run();
  }
}