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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*

fun main(args: Array<String>) {
    val scanner = Scanner(System.`in`)
    val n = scanner.nextInt()
    val x = scanner.nextLong()
    val burgerSize = arrayListOf(1L)
    val numOfPatty = arrayListOf(1L)
    for (i in 1..n) {
        burgerSize.add(burgerSize[i-1] * 2 + 3)
        numOfPatty.add(numOfPatty[i-1] * 2 + 1)
    }
    
    fun calc(n: Int, x: Long): Long {
        if (n == 0) return 1
        if (x <= n) return 0
        if (x == burgerSize[n]) return numOfPatty[n]

        val center = (burgerSize[n] + 1).div(2L)
        return when {
            x < center -> calc(n - 1, x - 1)
            x > center -> numOfPatty[n - 1] + 1 + calc(n - 1, x - burgerSize[n - 1] - 2)
            else -> numOfPatty[n - 1] + 1
        }
    }
    print(calc(n, x))
}