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 MultiWayIf #-}

module Main where

import Data.Word (Word64)
import Debug.Trace (trace)

-- abc115D

main :: IO ()
main = do
  [n,x] <- words <$> getLine
  print $ f (read n) (read x)

f :: Int -> Word64 -> Word64
f n x
  | n == 0                   = 1
  | x <= 1                   = 0
  | size (n-1) + 1 >= x      = f (n-1) (x -1)
  | otherwise                = pati n - f n (size n - x)

size :: Int -> Word64
size 0 = 1
size n = 3 + 2 * size (n-1)

pati :: Int -> Word64
pati 0 = 1
pati n = 1 + 2 * pati (n-1)