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: Wrong Answer)

n, eat = map(int, input().split())

pattiesCount = lambda level: (1 << (level + 1)) - 1
bunsCount = lambda level: (1 << (level + 1)) - 2
bothCount = lambda level: (1 << (level + 2)) - 3

# for i in range(51):
#     if bothCount(i) != pattiesCount(i) + bunsCount(i):
#         raise Exception()
#     print(i, '->', pattiesCount(i), bunsCount(i), bothCount(i))

def doit(level, eat):
    if level == 0:
        return int(eat == 1)
    both = bothCount(level)
    patties = pattiesCount(level)
    if eat == both + 1:
        return 1 + patties
    if eat > both:
        return 1 + patties + doit(level - 1, eat - 2 - both)
    return doit(level - 1, eat - 1)

print(doit(n, eat))