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(){
    long long n,x;
    cin>>n>>x;
    long long s=1,t=1;
    for(int i=0;i<n;i++) s=s*2+3,t=t*2+1;
    long long ans=0;
    while(x>0){
        if(s/2+1<=x){
            ans+=t/2+1;
            if(x==s) x=x-s/2-2;
            else x=x-s/2-1;
            s=s/2-1;
            t=t/2;
        }
        else{
            s=s/2-1;
            t=t/2;
            x=x-1;
        }
    }
    cout<<ans;
}