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)

# from typing import NamedTuple

# class Burger(NamedTuple):
#     total: int
#     patty: int

from collections import namedtuple

def solve(n, x, burgers, total_eaten, patty_eaten):
    if n == 0:
        total_eaten += 1
        patty_eaten += 1
        return total_eaten, patty_eaten

    # try to eat the entire current level
    tmp_total = burgers[n].total
    tmp_patty = burgers[n].patty
    if total_eaten + tmp_total < x:
        return total_eaten + tmp_total, patty_eaten + tmp_patty

    # eat the lower bun
    total_eaten += 1
    if total_eaten == x:
        return total_eaten, patty_eaten

    # eat the lower n - 1 th burger
    total_eaten, patty_eaten = solve(n - 1, x, burgers, total_eaten, patty_eaten)
    if total_eaten == x:
        return total_eaten, patty_eaten

    # eat the middle patty
    total_eaten += 1
    patty_eaten += 1
    if total_eaten == x:
        return total_eaten, patty_eaten

    # eat the upper n - 1 th burger
    total_eaten, patty_eaten = solve(n - 1, x, burgers, total_eaten, patty_eaten)
    if total_eaten == x:
        return total_eaten, patty_eaten

    # eat the upper bun
    # the program should not reach the current line because this mean n th burger is eaten (= eat the entire current level)
    total_eaten += 1
    return total_eaten, patty_eaten

def main():
    N, X = map(int, input().split())
    Burger = namedtuple('Burger', ['total', 'patty'])
    burgers = [Burger(total=1, patty=1)]
    for i in range(N):
        total = burgers[i].total
        patty = burgers[i].patty
        burger = Burger(total=3 + total*2, patty=1 + 2*patty)
        burgers.append(burger)
    # print(burgers)
    total_eaten, patty_eaten = 0, 0
    total_eaten, patty_eaten = solve(N, X, burgers, total_eaten, patty_eaten)
    print(patty_eaten)

if __name__ == '__main__':
    main()