p03209 AtCoder Beginner Contest 115 - Christmas
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.

Examples

Input

2 7


Output

4


Input

1 1


Output

0


Input

50 4321098765432109


Output

2160549382716056
```python
n,x = map(int,input().split())

a=[0]*n
p=[0]*n

a[0]=1
p[0]=1

for i in range(1,n):
  a[i]=3+2*a[i-1]
  p[i]=1+2*p[i-1]
  
def f(n,x):
  if n ==0:
    return 0 if x <= 0 else 1
  elif x <= 1+a[n-1]:
    return f(n-1,x-1)
  else:
    return p[n-1]+1+f(n-1,x-a[n-1]-2)

print(f(n,x))


```