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)

val pNum = LongArray(50 + 1) { 0L }
val pbNum = LongArray(50 + 1) { 0L }
fun main(args: Array<String>) {
    pNum[0] = 1
    pbNum[0] = 1
    for (i in 1..50) {
        pNum[i] = pNum[i - 1] * 2 + 1
        pbNum[i] = pbNum[i - 1] * 2 + 3
    }

    val (n, x) = readLongList()
    val ans = pan(n, x)
    println(ans)
}

// 食べたパティ・全体
fun pan(level: Long, eat: Long): Long {
    if (level == 0L) {
        return if (eat >= 1) 1L else 0
    }

    val next = level.toInt() - 1
    return if (eat <= 1 + pbNum[next]) {
        pan(next.toLong(), eat - 1)
    } else {
        pNum[next] + 1 + pan(level - 1, eat - (pbNum[next] + 2))
    }
}

fun readInteger() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntegerList() = readStringList().map(String::toInt)
fun readLongList() = readStringList().map(String::toLong)
fun readDoubleList() = readStringList().map(String::toDouble)