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,X = list(map(int,input().split()))

Ps = [1]*51
for i in range(1,N+1):
    Ps[i] = Ps[i-1]*2+1

#[total,パティ数]
burger = [[1]*2 for i in range(51)]

ans = 0
for i in range(1,51):
    burger[i][0] = burger[i-1][0]*2+3
    burger[i][1] = burger[i-1][1]*2+1

    if X <= burger[i][0]:
        while 0<X:
            X -= 1 #一番下のBを食う
            if X==0:
                break
            
            if burger[i-1][0]<=X:
                X -= burger[i-1][0]
                ans += burger[i-1][1]
            
                if 0<X: #中間のPを食う
                    X -= 1
                    ans += 1

            i -= 1
            if i == 0:
                if 0<X:
                    ans += 1
                #残りはパンだけ
                break

        print(ans)    
        break