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 (2.7.6) (judge verdict: Accepted)

g_memo = {0: 1}
h_memo = {0: 1}

def g(l):
    if not l in g_memo:
        g_memo[l] = 3 + 2*g(l-1)
    return g_memo[l]

def h(l):
    if not l in h_memo:
        h_memo[l] = 1 + 2*h(l-1)
    return h_memo[l]

def solve(l, x):
    if x <= 0:
        return 0
    if l == 0: # x > 0
        return 1
    if x >= g(l):
        return h(l)
    res = 0
    y = 1
    # f(l-1)
    res += solve(l-1, x-y)
    y += g(l-1)
    # P
    res += int(y < x)
    y += 1
    # f(l-1)
    res += solve(l-1, x-y)
    return res

n, x = map(int, raw_input().split())
print(solve(n, x))