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 Scala (2.11.7) (judge verdict: Accepted)


object Main extends App {

  import scala.io.StdIn._
  import scala.math._

  val Array(n, x) = readLine.trim.split(' ').map(_.toLong)
  println(
    patty(n.toInt, x)
  )
  def patty(level: Int, so: Long): Long = {
    level match {
      case 0 ⇒ if (so >= 1) 1L else 0L
      case _ if so <= 0 ⇒ 0L
      case _ ⇒
        numOfLevel(level - 1) match {
          case l if l + 2 <= so ⇒ pattyOfLevel(level - 1) + 1 + patty(level - 1, so - l - 2)
          case _ ⇒ patty(level - 1, so - 1)
        }

    }
  }
  def pattyOfLevel(level: Int): Long = {
    level match {
      case 0 ⇒ 1L
      case _ ⇒ pattyOfLevel(level - 1) * 2 + 1
    }
  }
  def numOfLevel(level: Int): Long = {
    level match {
      case 0 ⇒ 1L
      case _ ⇒ numOfLevel(level - 1) * 2 + 3
    }
  }


  implicit class Extenion[T](val value :T){
    def also(func: T ⇒ Unit): T = {
      func(value)
      value
    }
    def let[R](func: T ⇒ R): R = func(value)
  }
}