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: Runtime Error)

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

"""
　　レベルnの層数：a_0 = 1 , a_n = 2*a_(n-1)+3
レベルnのパティ数：b_0 = 1 , b_n = 2*b_(n-1)+1
"""

def thickness(n):
    if n == 0:
        return 1
    else:
        return 2 * thickness(n-1) + 3

def patty(n):
    if n == 0:
        return 1
    else:
        return 2 * patty(n-1) + 1

def ans(n,x):
    if n == 0:
        return 1
    else:
        if x == 1:
            return 0
        if 1 < x <= thickness(n-1)+1:
            return ans(n-1,x-1)
        if x == thickness(n-1) + 2:
            return patty(n-1) + 1
        if thickness(n-1) + 2 < x <= 2 * thickness(n) + 2:
            return patty(n-1) + 1 + ans(n-1,x-2-thickness(n-1))
        if x == 2 * thickness(n-1) + 3:
            return 2 * patty(n-1) + 1

print(ans(N,X))