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)


ans = 0
def count_ans(level, index, len_dic, p_dic):
    global ans
    if level == 0:
        ans += 1
    else:
        if index == 0:
            pass
        if index == len_dic[level] // 2:
            ans += 1
            ans += p_dic[level - 1]
        elif index == len_dic[level] - 1:
            ans += p_dic[level]
        elif index > len_dic[level] // 2:
            ans += p_dic[level - 1] + 1
            index_next = index - len_dic[level - 1] - 2
            count_ans(level - 1, index_next, len_dic, p_dic)
        else:
            index_next = index - 1
            count_ans(level - 1, index_next, len_dic, p_dic)


def get_len_dic(level):
    len_dic = [1]
    for i in range(level):
        len_dic.append(len_dic[-1] * 2 + 3)
    return len_dic

def get_p_dic(level):
    p_dic = [1]
    for i in range(level - 1):
        p_dic.append(p_dic[-1] * 2 + 1)
    return p_dic

def main():
    global ans
    level, eat_num = map(int, input().split())
    len_dic = get_len_dic(level)
    p_dic = get_p_dic(level)
    count_ans(level, eat_num - 1, len_dic, p_dic)
    print(ans)


if __name__ == '__main__':
    main()