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)

module Main where

import Control.Monad
import Data.List
import Debug.Trace
  
main :: IO ()
main = do
  [n, x] <- map read . words <$> getLine :: IO [Integer] -- (< 50, exp)
  print $ pat n x
  where
    pat 0 x = 1
    pat n x
      | x < 2 = 0
      | x < len (n-1) + 2 = pat (n-1) (x-1)
      | x < len (n-1) + 3 = 1 + pat (n-1) (x-1)
      | x < len n = 1 + pat (n-1) (x-1) + pat (n-1) (x-len(n-1)-2)
      | otherwise = 1 + pat (n-1) (x-1) * 2
    len 0 = 1
    len n = len (n - 1) * 2 + 3