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 len = LongArray(51, { 1L })
val nPans = LongArray(51, { 1L })

fun count(N: Int, X: Long): Long {
    val mid = (len[N]+1L)/2L
    return if(N==0 && X==1L) {
        1L
    } else if (X==1L) {
        0L
    }
    else if(X==len[N]) {
        nPans[N]
    } else if(X == mid) {
        nPans[N-1] + 1
    } else if (X < mid) {
        count(N - 1, X-1)
    } else if (X > mid){
        nPans[N-1] + count(N-1, X-mid) + 1
    } else {
        0L
    }
}


fun main(args: Array<String>) {
    val (N,X) = readLine()!!.split(" ").map { it.toLong() }
    val NN = N.toInt()

    // preprocessing
    for (i in 1 until 51) {
        len[i] = 2 * len[i-1] + 3
        nPans[i] = 2 * nPans[i-1] + 1
    }
//    assert(len[0] == 1L)
//    assert(len[1] == 5L)
//    assert(len[2] == 13L)
//    assert(nPans[0] == 1L)
//    assert(nPans[1] == 3L)
//    assert(nPans[2] == 7L)
//    assert(count(2, 1L) == 0L)
//    assert(count(2, 4L) == 2L)
//    assert(count(2, 7L) == 4L)
//    assert(count(2, 9L) == 5L)
//    assert(count(2, 10L) == 6L)
//    assert(count(2, 11L) == 7L)
//    assert(count(2, 13L) == 7L)
//    assert(count(50, 4321098765432109L) == 2160549382716056L)

    val ans = count(NN, X)
    println(ans)
}