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)

import numpy as np

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

a = 1
p = 1
a_list = [1]
p_list = [1]
for i in range(N+1):
    a = 2 * a + 3
    p = 2 * p + 1
    a_list.append(a)
    p_list.append(p)


def f(N, X):
    ai_1 = a_list[N-1]
    if X == 1:
        out = 0
    elif 2 <= X and X <= 1+ai_1:
        out = f(N-1, X-1)
    elif X == 2 + ai_1:
        out = p_list[N-1] + 1
    elif 3 + ai_1 <= X and X <= 2 + 2*ai_1:
        out = p_list[N-1] + 1 + f(N-1, X - 2 - a_list[N-1])
    elif X == 3+ 2*ai_1:
        out = p_list[N]
    else:
        raise Exception("bad")
    return out


print(f(N, X))