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)

# -*- coding: utf-8 -*-


def main():
    """Function."""
    n, x = map(int, input().split())

    total_len = [0 for _ in range(n + 1)]
    p_len = [0 for _ in range(n + 1)]
    total_len[0], p_len[0] = 1, 1

    for i in range(n):
        total_len[i+1] = total_len[i] * 2 + 3
        p_len[i+1] = p_len[i] * 2 + 1

    p_counter = 0
    del_counter = x

    for _ in range(n):
        if del_counter in total_len:
            p_counter += p_len[total_len.index(del_counter)]
            break
        elif del_counter+1 in total_len:
            p_counter += p_len[total_len.index(del_counter+1)]
            break

        # print(del_counter)
        temp_len, temp_p = 0, 0
        for i in range(n):
            if total_len[i+1] > x:
                temp_len = total_len[i]
                temp_p = p_len[i]
                break

        p_counter += (temp_p)
        del_counter += -(temp_len)

        if del_counter <= 0:
            break

    print(p_counter)

if __name__ == "__main__":
    main()