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)

N,X = gets.split.map(&:to_i)
MEMO = []
def content(n)
  return MEMO[n] unless MEMO[n].nil?
  if n == 0
    [1, 0]
  else
    before = content(n-1)
    value = [before[0]*2 + 1, before[1]*2 + 2]
    MEMO[n] = value
    value
  end
end

# P
# B P P P B
# B BPPPB P BPPPB B
# B BBPPPBPBPPPBB P BBPPPBPBPPPBB B
# returns number of P
def burger(n, x)
  burger_content = content(n)
  # puts "burger(#{n}, #{x}), #{burger_content.to_s}"
  burger_size = burger_content.inject(:+)
  half = (burger_size+1) / 2
  if x <= 1
    0
  elsif x < half
    burger(n-1, x-1)
  elsif x == half
    burger(n-1, x-2) + 1
  elsif x < burger_size
    burger(n-1, half-2) + burger(n-1, x-half) + 1
  elsif x == burger_size
    burger_content[0]
  else
    puts "Failed burger(#{n}, #{x})"
  end
end

puts burger(N, X)