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)

{-#LANGUAGE FlexibleContexts#-}
import Control.Monad.State
import Control.Monad.Reader
import Control.Arrow
-- import Control.Comonad
import Data.Maybe
import Data.List
import Data.Bool
import Data.Fixed
import Data.Tuple
import qualified Data.Map.Strict as M
import qualified Data.Array.IO as IA
import qualified Data.Vector as V

getIn = read <$> getLine :: IO Int
getIns = map read . words <$> getLine :: IO [Int]
getInt = read <$> getLine :: IO Integer
getInts = map read . words <$> getLine :: IO [Integer]

type Row = Integer
type Col = Integer
type Point = (Integer, Integer)

mmm = 1000000007
factorial 0 s = s
factorial n s = factorial (n - 1) (s * n)
fact' n = factorial n 1
fi = fromInteger

-- 
--
--
--
-- Xn = x^(n+1) - 3

burgurSize num = 2 ^ (num + 2) - 3
pattiNum num = 2 ^ (num + 1) - 1
eatableSize :: Integer -> Integer
eatableSize num = toInteger $ flip (-) 2 . truncate $ logBase 2 (fi num + 3) 

eat layer gabu
    | gabu < 1 = 0
    | layer == 1 = do
        if gabu > 5 then 3 + eat 1 (gabu - 6) + 1
        else if gabu < 2 then 0
        else min 3 $ gabu - 1
    | eatableSize gabu < layer = eat (layer - 1) (gabu - 1) -- gabuが-1なのは一番外側のバンズを食べないと内側のパティまで届かないから
    | otherwise = do
        let nokoriGabu = gabu - (burgurSize layer) - 1
        if nokoriGabu < 0 then pattiNum layer
        else pattiNum layer + eat layer nokoriGabu + 1 -- 最後の1はＮ−１バーガーの間に挟まるパティ

main = do
    [l, g] <- getInts
    putStrLn . show $ min (pattiNum l) (eat l g)