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: Accepted)

#include <iostream>
#include <algorithm>

using namespace std;

long long ans = 0;
long long len[100]={1};
long long b[100]={0};
long long p[100]={1};
void fun(long long L,long long X)
{
    //cout<<"L = "<<L<<" "<<"x = "<<X<<endl;
    if(L==0&&X){ans++;
    return;}
    if(X==len[L-1]+2){
        //cout<<"if1"<<endl;
        ans+=p[L-1];
        ans++;
        return;

    }
    else if(X>1&&X<=1+len[L-1]){
         //cout<<"if2"<<endl;
        fun(L-1,X-1);
    }
    else if(X==1){
         //cout<<"if3"<<endl;
        return;
    }
    else if(X>=len[L-1]+3&&X<=len[L]-1){
         //cout<<"if4"<<endl;
        ans+=p[L-1];
        ans++;
        fun(L-1,X-2-len[L-1]);
    }
    else if(X==len[L]){
       //  cout<<"if5"<<endl;
        ans+=p[L];
        return;
    }
}
int main()
{
    long long N,X;
    cin >> N >> X;

    for(int i = 1 ; i < 55 ; i ++)
    {
        len[i] = len[i-1]*2+3;
        b[i] = b[i-1]*2+2;
        p[i] = len[i]-b[i];
    }
    //cout<<"len50 = "<<len[50]<<endl;
    fun(N,X);
    cout<<ans<<endl;
	return 0;
}