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: Accepted)

# Title: Christmas
# Link: https://abc115.contest.atcoder.jp/tasks/abc115_d

import sys


sys.setrecursionlimit(10 ** 6)

read_list_int = lambda: list(map(int, sys.stdin.readline().strip().split(' ')))


def f(n: int, x: int, a: list, p: list):
    if n == 0 and x == 0:
        return 0
    elif n == 0:
        return 1
    elif x == 1:
        return 0
    elif 1 < x <= 1 + a[n-1]:
        return f(n-1, x-1, a, p)
    elif x == 2 + a[n-1]:
        return p[n-1] + 1
    elif 2+a[n-1] < x <= 2+2*a[n-1]:
        return p[n-1]+1+f(n-1, x-(2+a[n-1]), a, p)
    elif x == 3 + 2*a[n-1]:
        return 2*p[n-1]+1


def solution(n: int, x: int):
    a = [1] + [0]*n
    p = [1] + [0]*n

    for i in range(1, n+1):
        a[i] = 2*a[i-1] + 3
        p[i] = 2*p[i-1] + 1
    
    return f(n, x, a, p)



def main():
    n, x = read_list_int()
    print(solution(n, x))


if __name__ == '__main__':
    main()