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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define LL long long
#define Max 100005
#define Mod 1e9+7
const LL mod=1e9+7;
const LL inf=0x3f3f3f3f;
using namespace std;
int main()
{
	LL n,x;
	LL siz[52],eat[52];
	siz[0]=eat[0]=1;
	for(int i=1;i<=50;i++)
	{
		siz[i]=siz[i-1]*2+3;
		eat[i]=eat[i-1]*2+1;
	}
	scanf("%lld%lld",&n,&x);
	LL ans=0;
	for(int i=1;i<=n;i++)
	{
		if(x==0)
			break;
		else if(x==siz[i])
		{
			ans+=eat[i];
			break;
		}
		if(x==1)
			break;
		assert(i>0);
		if(x<=(siz[i-1]+1))
		{
			x--;
		}
		else
		{
			ans+=(eat[i]+1);
			x-=(siz[i-1]+2);
		}
	}
	printf("%lld\n",ans);
    return 0;
}