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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program test
implicit none

integer(8)::n,x,a
integer(8):: i,j,k,fib(0:50),pat(0:50),level

read(*,*) n,x

	fib(0) = 1
	pat(0) = 1
	do i=1,50
		fib(i) = 2*fib(i-1)+3
		pat(i) = 2*pat(i-1)+1
	enddo

a =  ans(n,x)

write(*,*) a

!もし下からの指定された層数がハンバーガーの半分をこえていたら、パティ層数から、指定されてない部分を引く


!そうでなければ、レベルn-1バーガーの、x-1層目までのパティ数を数える

contains

recursive integer(8) function ans(n,x) result(res)
	implicit none
	integer(8):: n,x

	if(x==0) then
		res = 0
	else if(n==0 .and. x==1)then
		res = 1
	else if(2*x > fib(n))then
		res = pat(n) - ans(n,fib(n)-x)
	else
		res = ans(n-1,x-1)
	endif
	
	return
	
end function

end program