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 (2.4.0) (judge verdict: Wrong Answer)


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

nlen = [0] * (N+1)
nlen[0] = 1

for i in range(N):
    i += 1

    nlen[i] = 3 + nlen[i-1] * 2

    
    
num = [0] * (N+1)

p = 0
b = 0

amari = X


for i in range(N):

    i = N-i

    num[i-1] += 2 * num[i]
    p += num[i]
    b += num[i] * 2

    if 3 + 2 * nlen[i-1]  == amari :

        num[i-1] += 2

        p += 1
        b += 2

        amari = 0

    elif 2 + 2 * nlen[i-1] == amari:

        num[i-1] += 2

        p += 1
        b += 1

    elif 2 + nlen[i-1] <= amari:

        num[i-1] += 1

        p += 1
        b += 1

        amari -= 2 + nlen[i-1]

    elif 1 + nlen[i-1] == amari:

        num[i-1] += 1

        b += 1

        amari = 0

    elif 1 <= amari:

        b += 1
        amari -= 1

print (p + num[0])