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 lint = long long;
lint N, X;

lint rec(lint N, lint X){
  if(N == 0) return 1;
  if(X == 1) return 0;
  lint len = (1LL << N + 1)  - 3;
  lint p =  (1LL << N) - 1;
  if(1 < X && X <= 1 + len) return rec(N - 1, X - 1);
  if(X == 2 + len) return p + 1;
  if(2 + len <= X && X <= 2 * len + 2) return p + 1 + rec(N - 1, X - len - 2);
  if(X == 2 * len + 3) return 2 * p + 1;
}

signed main(){
  cin >> N >> X;
  cout << rec(N, X) << endl;
}