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: Accepted)

line = [int(x) for x in input().strip().split()]

N = line[0]
X = line[1]


patties = [1]
buns = [0]
layers = [1]
for i in range(1, 51):
	patties.append(patties[i - 1] * 2 + 1)
	buns.append(buns[i - 1] * 2 + 2)
	layers.append(patties[i] + buns[i])

def answer(l, r, level):
	if (l > r):
		return 0
	if (l == 1 and r == layers[level]):
		return patties[level]

	mid = layers[level] // 2 + 1
	ans = 0
	if (r > mid):
		ans += 1
		ans += answer(1, layers[level - 1], level - 1)
		ans += answer(1, r - mid, level - 1)
	elif (r == mid):
		ans += 1
		ans += answer(1, layers[level - 1], level - 1)
	else:
		ans += answer(1, r - 1, level - 1)
	return ans

print(answer(1, X, N))