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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import sys
sys.setrecursionlimit(10**9)

def mi(): return map(int,input().split())
def ii(): return int(input())
def isp(): return input().split()
def deb(text): print("-------\n{}\n-------".format(text))

INF=10**20
def main():
    N,X=mi()

    stack = [(N,X)]
    res = 0
    while stack:
        n,x = stack.pop()
        if n == 0: return 1
        c = 2**(n+2)-3
        half = c//2

        if x <= half:
            if x == 1:
                res += 0
            else:
                stack.append((n-1,x-1))
        elif x == half+1:
            res += 2**(n-1+1) - 1 + 1
        elif x < c:
            stack.append((n-1,x-(half+1)))
            res += 2**(n-1+1) - 1 + 1
        else:
            assert x == c
            res += 2**(n+1)-1


    print(res)



if __name__ == "__main__":
    main()