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[] pnumInL;
    static long[] lenL;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long x = sc.nextLong();
        sc.close();

        pnumInL = new long[n+1];
        lenL = new long[n+1];
        pnumInL[0] = 1;
        lenL[0] = 1;
        for(int i=0; i<n; i++){
            pnumInL[i+1] = pnumInL[i] * 2 + 1;
            lenL[i+1] = lenL[i] * 2 + 3;
        }

        System.out.println(culcPnum(n, 1, x));
    }

    public static long culcPnum(int level, long start, long end){
        long mlen = end - start + 1;
        if(level == 0 && mlen == 1) return 1;
        if(mlen <= 1) return 0;
        if(mlen >= lenL[level]-1) return pnumInL[level];
        if(mlen >= lenL[level-1] + 2){
            return pnumInL[level-1] + 1 + culcPnum(level-1, start + lenL[level-1]+2, end);
        }else{
            return culcPnum(level-1, start+1, end);
        }
    }
}