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 Lua (5.3.2) (judge verdict: Accepted)

local n = io.read("n")
local k = io.read("n")
-- local n, k = 1, 1
local g = {[0] = {1, 1}}
for i = 1, n do
	local c0 = g[i - 1][1]
	local p0 = g[i - 1][2]
	local c = c0 * 2 + 3
	local p = p0 * 2 + 1
	g[i] = {c, p}
end
local function f(_n, _k)
	if _k <= 0 then
		return 0
	end
	if _n <= 0 then
		return 1
	end
	local c = g[_n][1]
	local hc = (g[_n][1] + 1) // 2
	if _k >= c then
		return g[_n][2]
	elseif _k == hc then
		return f(_n - 1, _k - 2) + 1
	elseif _k < hc then
		return f(_n - 1, _k - 1)
	else
		return g[_n - 1][2] + 1 + f(_n - 1, _k - hc)
	end
end
print(f(n, k))