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 Ruby (2.3.3) (judge verdict: Wrong Answer)

$a = {}
def all(n)
  return 1 if n == 0
  return $a[n] if $a[n]
  $a[n] = 3 + 2*all(n-1) 
end

$b = {}
def patall(n)
  return 1 if n == 0
  return $b[n] if $b[n]
  $b[n] = 1 + 2*patall(n-1)
end

def pat(n, x)
  return 0 if x <= 0
  return patall(n) if all(n) == x

  return pat(n-1,x-1) if 1+all(n-1) >= x

  r = 0
  r += patall(n-1)
  x -= 1+all(n-1)
  return r if x == 0
  r += 1
  x -= 1

  if all(n-1) <= x
    r += patall(n-1)
    return r
  else
    r += pat(n-1, x)
    return r
  end
end

n,x=gets.split.map(&:to_i)
puts all(n)
puts pat(n,x)