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: Wrong Answer)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE TupleSections #-}

module Main where

import           Data.List
import           Control.Monad
import           Debug.Trace
import qualified Data.ByteString.Char8         as BC
import           Data.Maybe                     ( fromJust, fromMaybe )
import qualified Data.Set                      as S
import qualified Data.IntMap.Strict            as IM
import qualified Data.IntMap.Lazy            as IML
import qualified Data.Map.Strict               as M
import           Data.Char
import qualified Data.Array.IArray as A
import qualified Data.Array.Unboxed as UA
import Data.Bits
import Control.Monad.State.Strict
import qualified Data.Array.ST as STA
import qualified Data.Array.IO as IOA
import qualified Data.Array.MArray as MA
import Control.Monad.ST
import System.IO (stdin)
import Control.Arrow
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as UV
import qualified Data.Vector.Generic as GV
import qualified Data.Vector.Mutable as MV
import Data.Ix
import Data.Ord (Down(Down))
import qualified Data.Sequence as Seq
import Data.Foldable (toList)
import Data.Fixed

debug = False

ts :: Show a => a -> a
ts a = if debug then traceShowId a else a


readTuple2 :: IO (Int, Int)
readTuple2 = do
    [a, b] <- readInts
    return (a, b)

readTuple3 :: IO (Int, Int, Int)
readTuple3 = do
    [a, b, c] <- readInts
    return (a, b, c)


readInt :: IO Int
readInt = fst . fromJust . BC.readInt <$> BC.getLine

readInts :: IO [Int]
readInts = map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine

readIntV :: Int -> IO (UV.Vector Int)
readIntV n = GV.unfoldrN n (fmap (fmap BC.tail) . BC.readInt) <$> BC.getLine

readIntegersV :: Int -> IO (V.Vector Integer)
readIntegersV n = GV.unfoldrN n (fmap (fmap BC.tail) . BC.readInteger) <$> BC.getLine

readIntegers :: IO [Integer]
readIntegers = map (fst . fromJust . BC.readInteger) . BC.words <$> BC.getLine

split :: (a -> Bool) -> [a] -> [[a]]
split f [] = []
split f as =
    let (fo, la) = span f as
        las      = case la of
            [] -> []
            xs -> split f $ tail xs
    in  case fo of
            [] -> las
            xs -> xs : las


solve :: Int -> Int -> Int
solve n x = getPatty n x where
  layers :: UV.Vector Int
  layers = ts $ GV.unfoldrN (n + 1) (\prev -> Just (prev, prev * 2 + 3)) 1
  patties :: UV.Vector Int
  patties = ts $ GV.unfoldrN (n + 1) (\prev -> Just (prev, prev * 2 + 1)) 1
  getPatty :: Int -> Int -> Int
  getPatty 0 n = n
  getPatty i x
    | x == half = patties GV.! (i - 1) + 1
    | x < half = getPatty (i - 1) (x - 1)
    | otherwise = patties GV.! (i - 1) + 1 + getPatty (i - 1) (x - half) where
    layerNum = layers GV.! i
    half = layerNum `div` 2 + 1


main :: IO ()
main =
  readTuple2 >>= print . uncurry solve