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>
using namespace std;
using LL=long long;
LL get(int level,LL h){
  if(level==0)return 1;
  LL s=pow(LL(2),level+2)-3;
  if(h==1)return 0;
  if(h==s)return pow(LL(2),level+1)-1;
  if(h<=(s-1)/2)return get(level-1,h-1);
  if(h==(s+1)/2)return get(level-1,(s-1)/2-1)+1;
  return get(level-1,(s-1)/2-1)+1+get(level-1,h-(s+1)/2);
}
int main(){
  int N;LL X;cin>>N>>X;
  cout<<get(N,X)<<endl;
}