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 Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {
	private def direct(a: Int, n: Int): Long = {
		//val pow = Math.pow(2, n).toLong
		val pow = 1L << n
		pow + a * (pow - 1)
	}

	//@scala.annotation.tailrec
	private def func(n: Int, x: Long): Long = {
		//println("func", n, x)
		if (n == 0 && x > 0) return 1L
		if (x <= 1) return 0L
		//if (n == 0 && x == 0) return 0L

		val lenOfN1 = direct(3, n - 1)
		val numOfN1 = direct(1, n - 1)

		if (x <= lenOfN1 + 1) {
			func(n - 1, x - 1)
		} else {
			numOfN1 + 1 + func(n - 1, x - 2 - lenOfN1)
		}
	}

	private def solve(in: Seq[Long]): Long = func(in(0).toInt, in(1))

	assert(solve(Seq(0, 0)) == 0)
	assert(solve(Seq(0, 1)) == 1)
	assert(solve(Seq(1, 1)) == 0)
	assert(solve(Seq(3, 14)) == 7)
	assert(solve(Seq(3, 15)) == 8)
	assert(solve(Seq(3, 28)) == 15)
	assert(solve(Seq(3, 29)) == 15)
	assert(solve(Seq(50, 4321098765432109L)) == 2160549382716056L)
	println(solve(io.Source.stdin.getLines.toIndexedSeq.head.split(' ').map(_.toLong)))
}