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)

Tmp = []
Tmp = input().rstrip().split(' ')
 
nN = int(Tmp[0])
nX = int(Tmp[1])
 
nA = 1
nP = 1
 
nAnsA = []
nAnsP = []
 
for i in range(nN):
  nTmpA = nA * 2 +3
  nTmpP = nP * 2 +1
  nAnsA.append(nTmpA)
  nAnsP.append(nTmpP)
  nA = nTmpA
  nP = nTmpP

nAnsA.sort(reverse=True)  
nAnsP.sort(reverse=True)  
  
nMaxA = nAnsA[0]
nMaxP = nAnsP[0]
 
nTmpA = nMaxA
nTmpP = nMaxP
 
nAns = 0
for i in range(nN):
  nTmpA = nTmpA // 2 + 1
  nTmpP = nTmpP // 2 + 1
  
  if nTmpA > nX:
    nTmpA -= 2
    nTmpP -= 1
    nX -= 1
  elif nTmpA == nX:
    nAns += nTmpP
    break
  else:
    nAns += nTmpP
    nX -= nTmpA
    nTmpA -= 2
    nTmpP -= 1
    
print(nAns)