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: Accepted)

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

m = 1
p = 1
LMAP = [1]
PMAP = [1]
n.times do
  m = 3 + m * 2
  p = 1 + p * 2
  LMAP << m
  PMAP << p
end

def count(l, a)
  return 0 if a == 0
  if l == 1
    return 3 if a == 5
    return a - 1
  end

  center = LMAP[l-1] + 1

  if a < center
    count(l-1,a-1)
  elsif a == center
    PMAP[l-1]
  elsif a == center + 1
    PMAP[l-1] + 1
  elsif a == LMAP[l]
    PMAP[l]
  else # a > center + 1
    PMAP[l-1] + 1 + count(l-1,a-(center+1))
  end
end

p count(n,x)