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;
map<pair<ll,ll>,ll> mp;
ll f(ll i,ll x) {
  if(mp.count({i,x})) return mp[{i,x}];
  if(!x--) return 0;
  if(!i--) return 1;
  ll a=(1LL<<i+2)-3;
  ll res;
  if(!x) res=0;
  else if(x<a+1) res=f(i,x);
  else res=f(i,a)+f(i,x-a-1)+1;
  mp[{i+1,x+1}]=res;
  return res;
}
int main(){
  ll n,x;
  cin>>n>>x;
  cout<<f(n,x)<<endl;
}
