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
import java.util.*;
public class Main{
  static long[] d;
  static long[] cnt;
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    d = new long[n+1];
    cnt = new long[n+1];
    d[0]=1;
    cnt[0]=1;
    for(int i=1;i<=n;i++){
      d[i]=2*d[i-1]+3;
      cnt[i]=2*cnt[i-1]+1;
    }
    long x = sc.nextLong();
    long p = find(n,x);
    System.out.println(p);
  }
  static long find(int n,long x){
    if(n==0&&x>0)return 1;
    else if(n==0)return 0;
    else if(x<=d[n-1]+1)return find(n-1,x-1);
    else return cnt[n-1]+1+find(n-1,x-2-d[n-1]);
  }
}