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.*;

class Main {
    class Cache {
        private long size;
        private long pati;

        public Cache(long size, long pati) {
            this.size = size;
            this.pati = pati;
        }

        public long size() {
            return this.size;
        }

        public long pati() {
            return this.pati;
        }
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String[] line = scanner.nextLine().split(" ", 2);
        long n = Long.parseLong(line[0]);
        long x = Long.parseLong(line[1]);
        new Main(x, 0).main(n);
    }

    private long toEat;
    private long pati;
    private HashMap<Long, Cache> cacheMap;

    public Main(long toEat, long pati) {
        this.toEat = toEat;
        this.pati = pati;
        this.cacheMap = new HashMap<>();
    }

    public void main(long level) {
        this.eat(level);
        System.out.println(this.pati);
    }

    public void eat(long level) {
        if (toEat == 0) {
            return;
        }

        if (level == 0) {
            this.toEat--;
            this.pati++;
        } else {
            Cache cache = this.cacheMap.get(level - 1);

            long initToEat = this.toEat;
            long initPati = this.pati;

            this.toEat--; // ban

            // level - 1 burger
            if (cache != null && this.toEat >= cache.size) {
                this.toEat -= cache.size;
                this.pati += cache.pati;
            } else if (this.toEat > 0) {
                this.eat(level - 1);
            }

            if (this.toEat > 0) { // pati
                this.toEat--;
                this.pati++;
            }

            // level - 1 burger
            if (cache != null && this.toEat >= cache.size) {
                this.toEat -= cache.size;
                this.pati += cache.pati;
            } else if (this.toEat > 0) {
                this.eat(level - 1);
            }

            if (this.toEat > 0) { // ban
                this.toEat--;

                this.cacheMap.put(level, new Cache(initToEat - toEat, pati - initPati));
            }
        }
    }
}
