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>
inline long long sum_layer(int n){
    return (1LL<<(n+2))-3;
}
inline long long sum_patty(int n){
    return (1LL<<(n+1))-1;
}
long long num_patty(int n,long long x){
    if(x==0)return 0;
    if(n==0)return 1;
    if(x<=sum_layer(n-1)+1)return num_patty(n-1,x-1);
    return sum_patty(n-1)+1+num_patty(n-1,x-sum_layer(n-1)-2);
}
int main(){
    int n;
    long long x;
    scanf("%d%lld",&n,&x);
    printf("%lld",num_patty(n,x));
    return 0;
}