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)

fun main(arr:Array<String>) {
    dic.add(1)
    patDic.add(1)
    for(i in (1..50)) {
        dic.add(dic.last() * 2 + 3)
        patDic.add(patDic.last() * 2 + 1)
    }
    val (n,x) = readLine()!!.split(" ").map { it.toLong() }
    val ans = getAns(x, n.toInt())
    println(ans)
}

fun getAns(remain:Long, depth:Int):Long {
    if(remain == 0L) {
        return 0
    }
    if(depth == 0) {
        return 1
    }
    if(remain - 1 <= dic[depth - 1]) {
        return getAns(remain - 1, depth - 1)
    }
    if(remain - 1 == dic[depth-1] + 1 ) {
        return patDic[depth-1] + 1
    }
    if(remain - 1 < dic[depth-1]*2 + 1) {
        return patDic[depth-1] + 1 + getAns(remain - 2 - dic[depth-1], depth - 1)
    }
    return patDic[depth]
}

val dic = mutableListOf<Long>()
val patDic = mutableListOf<Long>()