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<stdio.h>
#define fo(i,a,b) for(int i=a;i<=b;i++)
int n;
unsigned long long f[60],g[60],x,ans;
void dfs(int a){
	if (a==0){
		if (x==1) ans++;
		return;
	}
	if (x){
		x--;
		if (x>=f[a-1]){
			x-=f[a-1];
			ans+=g[a-1];
			if (x){
				x--;
				ans++;
				if (x>=f[a-1]) ans+=g[a-1];else dfs(a-1);
			}
		}else dfs(a-1);
	}
}
int main(){
	scanf("%d%llu",&n,&x);
	f[0]=g[0]=1;
	fo(i,1,n){
		f[i]=f[i-1]*2+3;
		g[i]=g[i-1]*2+1;
	}
	dfs(n);
	printf("%llu\n",ans);
	return 0;
}