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 Ruby (2.3.3) (judge verdict: Accepted)

n, x = gets.split.map &:to_i

mod = []

def x(p)
	2 * p + 3
end

seed = 1

n.times{
	seed = x(seed)
	mod << seed
}

mod.reverse!

count = 0

if x == mod[0] then
	puts mod[0] / 2 + 1
	exit
end

mod[1..-1].each{ |m|
	if x >= 2 * m + 2 then
		count += 2 * (m / 2 + 1) + 1
		x = 0
		break
	elsif x >= m + 1 then
		if x >= m + 2 then
			x -= 1
			count += 1
		end

		count += (m / 2 + 1)
		x -= m
	end
	
	x -= 1
}

if x >= 2 then
	count += 1
end

if x >= 3 then
	count += 1
end

if x >= 4 then
	count += 1
end

puts count