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.

Examples

Input

2 7


Output

4


Input

1 1


Output

0


Input

50 4321098765432109


Output

2160549382716056
#include <iostream>
#include <algorithm>
using namespace std;
int main(void){
    long long n,x,p[64],q=0;
    cin>>n>>x;
    x--;
    p[0]=1;
    for(int i=1;i<64;i++){
        p[i]=p[i-1]*2;
    }
    for(long long i=n;i>=0;i--){
        //cout<<q<<endl;
        if(x==p[i+2]-4){
            q+=p[i+1]-1;
            i=0;
        }else if(x>=p[i+1]-2){
            q+=p[i]-1+1;
            //if(x==p[i+1]-2)q++;
            x-=p[i+1]-3+2;
        }else{
            x--;
        }
    }
    cout<<q<<endl;
}
