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)

import qualified Data.ByteString.Lazy.Char8 as B
import Data.Maybe
import Data.List
import qualified Data.Vector.Unboxed as VU

solve :: Int -> Int -> Int
solve 0 0 = 0
solve 0 1 = 1
solve n x
  | x <= 1
  = 0
  | x <= 1 + lPrev
  = solve (n-1) (x-1)
  | x == 1 + lPrev + 1
  = pPrev + 1
  | x <= 1 + lPrev + 1 + lPrev
  = pPrev + 1 + solve (n-1) (x - (1 + lPrev + 1))
  | x == 1 + lPrev + 1 + lPrev + 1
  = pPrev + 1 + pPrev
  where lPrev = nLayer VU.! (n-1)
        pPrev = nPatty VU.! (n-1)

nLayer :: VU.Vector Int
nLayer = VU.fromListN 51 $ unfoldr f 1
  where f k = Just (k, 2*k + 3)

nPatty :: VU.Vector Int
nPatty = VU.fromListN 51 $ unfoldr f 1
  where f k = Just (k, 2*k + 1)

readBInt :: B.ByteString -> Int
readBInt = fst . fromJust . B.readInt

tmain :: B.ByteString -> Int
tmain cont =
  let remLines0 = map B.words (B.lines cont)
      [bs_n,bs_x]:remLines1 = remLines0
      n = readBInt bs_n
      x = readBInt bs_x
  in solve n x

outAnswer :: Int -> IO ()
outAnswer = putStrLn . show

main :: IO ()
main = outAnswer . tmain =<< B.getContents