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 Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

var n:integer;
x,ans:int64;
procedure find(i:integer);
begin 
	if x<=3 then 
	begin 
		ans:=ans+x;
		x:=0;
	end;
	if x>3 then 
	begin 
		ans:=ans+3;
		x:=x-3;
		if x<=i then 
		begin 
			x:=0;
		end;
		if x>i then 
		begin 
			ans:=ans+1;
			x:=x-i-1;
			if x<=i then x:=0;
			if x>i then x:=x-i;
		end;
	end;
end;
procedure p(y:integer);
begin 
	if y>1 then p(y-1);
	find(y);
	if x=0 then begin write(ans);halt;end;
	if y>1 then p(y-1);
end;
begin 
	read(n);read(x);
	ans:=0;
	x:=x-n;
	if x>0 then 
		p(n-1);
	write(ans);
end.