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 Python (3.4.3) (judge verdict: Accepted)

#!/usr/bin/env python3
# -*- coding:utf-8 -*-

P = True
B = False
lenP = lambda x: 2*x + 1
lenB = lambda x: 2*x + 2
lenS = lambda x: 2*x + 3

def main():
  n, x = map(int, input().split())
  _next = lambda burger: [B] + burger + [P] + burger + [B]
  burger = [P]
  Pn = {0:1}
  Bn = {0:0}
  Sn = {0:1}
  for i in range(n):
    Pn[i+1] = lenP(Pn[i])
    Bn[i+1] = lenB(Bn[i])
    Sn[i+1] = lenS(Sn[i])
  _sum = 0
  middle = int((Sn[n] + 1)/2)
  for i in list(range(1, n+1))[::-1]:
    if middle == x:
      _sum += int(Pn[i-1])
      break
    elif middle < x:
      _sum += Pn[i-1] + 1
      middle += int((Sn[i-1]+1)/2)
    else:
      middle -= int((Sn[i-1]+1)/2)
      pass
  if middle <= x:
    _sum += 1

  print(_sum)

  pass

if __name__=='__main__':
  main()