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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

countPatty :: Int -> Int -> Int
countPatty n x = p
    where (t, p) = burger (prep n) (x, 0)

burger :: [(Int,Int)] -> (Int, Int) -> (Int, Int)
burger _ (0, ac) = (0, ac)
burger ((t, p):st) (x, ac)
    | x >= t      = (x-t, ac + p) 
    | otherwise = (bun.burger st.patty.burger st.bun) (x, ac)

bun :: (Int, Int) -> (Int, Int)
bun (0, ac) = (0, ac)       
bun (x, ac) = (x-1, ac)

patty :: (Int, Int) -> (Int, Int)
patty (0, ac) = (0, ac)
patty (x, ac) = (x-1, ac+1)

prep :: Int -> [(Int, Int)] 
prep 0 = [(1, 1)]
prep m = (2*t+3, 2*p+1):xs
    where
        (t, p) = head xs
        xs = prep (m-1)
    
main :: IO() 
main = do
    line1 <- getLine
    let [stN, stX] = words line1
        n = read stN :: Int
        x = read stX :: Int
    let ans = countPatty n x 
    print ans