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 <bits/stdc++.h> 

#define INF INT_MAX/2
#define MOD 1000000007

using namespace std;

using ll = long long;
using ull = unsigned long long;

vector<ull>two(52);

ull func(ull N,ll X){
   if(X <= 0) return 0;
   else if(X <= two[N+1]-2) return func(N-1,X-1); 
   else return func(N-1,X-two[N+1]+1)+two[N];
} 

int main(){
   ios::sync_with_stdio(false);
   cin.tie(0);

   two[0] = 1;
   for(int i=1;i<=51;i++)two[i] = 2*two[i-1];

   ull N,X;
   cin>>N>>X;
   cout<<func(N,X)<<endl;
   return 0; 
}
