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>
using namespace std;
#define ll long long

int N;
ll X;
ll a[50],p[50];

ll fact(int n,ll x){
  if(n==0) return 1;
  if(x==1) return 0;
  if(x<=1+a[n-1]) return fact(n-1,x-1);
  if(x==2+a[n-1]) return p[n-1]+1;
  if(x<=2*a[n-1]+2) return p[n-1]+1+fact(n-1,x-a[n-1]-2);
  if(x==2*a[n-1]+3) return p[n-1]*2+1;
}
int main(){
  cin>>N>>X;
  a[0]=p[0]=1;
  for(int i=1;i<N;i++){
    a[i]=2*a[i-1]+3;
    p[i]=2*p[i-1]+1;
  }
  cout<<fact(N,X)<<endl;
  return 0;
}