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<iostream>
#include<vector>
#include<string>
#include<algorithm>
#include<climits>
#include<queue>
#include<stack>
#include<cmath>

int main(){
	int n;
	long long x;
	long long x_;

	long long sum=0;
	std::cin>>n>>x;
	x_= x;

	std::vector<long long> aList;
	std::vector<long long> bList;
	std::vector<bool> useList;

	aList.resize(n+1);
	bList.resize(n+1);
	useList.resize(n, false);

	aList[0]=1;
	bList[0]=1;
	for(int i=1; i<n+1; i++)
		aList[i]= 3+ aList[i-1]*2;

	for(int i=1; i<n+1; i++)
		bList[i]= 1+ bList[i-1]*2;

	if(n==0){
		std::cout<<1<<std::endl;
		return 0;
	}

	x_-=1;
	for(int i=n-1; i>=0; i--){
		if(aList[i]<x_){
			x_-=aList[i];
			sum+=bList[i];
			useList[i]=true;
			if(x_>0){
				x_--;
				sum++;
				i++;
				if(useList[i])
					sum--;
			}
		}
		else{
			if(x_>0)
				x_--;
		}
	}

	std::cout<<sum<<std::endl;



	return 0;	
}