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 (1.3.71) (judge verdict: Accepted)

fun longList() = readLine()?.split(" ")?.map(String::toLong) ?: TODO()
fun main() {
    val (n, x) = longList()
    val ni = n.toInt()
    val m = Array(n.toInt() + 1) { 0L }
    fun create(l: Int): Long {
        if (l == 0) {
            return 1
        }
        if (m[l] > 0L) {
            return m[l]
        }
        return (create(l - 1) * 2 + 3).also {
            m[l] = it
        }
    }

    fun eatCount(n: Int, x: Long): Long {
        if (n < 0) {
            return 0L
        }
        val layer = create(n)
        if (x == layer) {
            return layer / 2 + 1
        }
        val center = layer / 2;
        return when {
            x <= center -> {
                eatCount(n - 1, x - 1)
            }
            x == center + 1 -> {
                return center / 2 + 1
            }
            else -> {
                eatCount(n - 1, center - 1) + eatCount(n - 1, x - center - 1) + 1
            }
        }
    }
    println(eatCount(ni, x).toString())
}