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<cstdio>

long long int blength(long long int n) {
    return (1LL<<(n+2)) - 3;
}

long long int func(long long int n, long long int x) {
    if (n == 0) {
        if (x == 1) return 1;
        else return 0;
    }
    if (x <= 1 + blength(n-1)) {
        return func(n-1, x-1);
    } else {
        return ( (1LL<<(n+1)) - 1 ) - func(n, blength(n)-x);
    }
}
int main() {
    long long int n, x;

    scanf("%lld%lld", &n, &x);
    printf("%lld\n", func(n, x));

    return 0;
}
