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 (3.8.2) (judge verdict: Accepted)

N,X = map(int, input().split())
burger = [(1,0)]
prev = (1,0)
for i in range(N):
    burger.append((2*prev[0]+1, 2*prev[1]+2))
    prev = burger[-1]

lev = N
cur = X-1
ps = 0
for i in range(N+1):
    if lev == 0:
        ps += 1
        break

    if cur == 0:
        break
    elif cur == sum(burger[lev-1])+1:
        ps += burger[lev-1][0]+1
        break
    elif cur == sum(burger[lev])-1:
        ps += 2*burger[lev-1][0] + 1
        break

    if cur < sum(burger[lev])/2:
        cur -= 1
        lev -= 1
    else:
        ps += burger[lev-1][0] + 1
        cur -= sum(burger[lev-1]) + 2
        lev -= 1
print(ps)