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 function memoize(f)
    local cache = {}
    local function key(...)
        local args = {...}
        local k = tostring(args[1])
        for i=2,#args do
            k = k .. "*" .. tostring(args[i])
        end
        return k
    end
    return function(...)
        local k = key(...)
        if cache[k] then
            return cache[k]
        end
        local r = f(...)
        cache[k] = r
        return r
    end
end

local thickness
thickness = memoize(function(n)
    if n == 0 then
        return 1
    else
        return 2 * thickness(n-1) + 3
    end
end)

local patties
patties = memoize(function (n, x)
    if n == 0 then
        return 1
    end
    local th_upper = thickness(n-1)
    if x == 1 then
        return 0
    elseif x <= th_upper + 1 then
        return patties(n-1, x-1)
    elseif x == th_upper + 2 then
        return 1 + patties(n-1, th_upper)
    else
        return 1 + patties(n-1, th_upper) + patties(n-1, x-2-th_upper)
    end
end)

local N, X = io.read("n", "n")
print(patties(N,X))