Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

2 7

Sample Output 1

4

There are 4 patties in the bottom-most 7 layers of a level-2 burger (BBPPPBPBPPPBB).

Sample Input 2

1 1

Sample Output 2

0

The bottom-most layer of a level-1 burger is a bun.

Sample Input 3

50 4321098765432109

Sample Output 3

2160549382716056

A level-50 burger is rather thick, to the extent that the number of its layers does not fit into a 32-bit integer.

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>

long long at[51]={1};
long long pat[51]={1};
long long ans=0;

int am(long long x,int level){
		//printf("%lld,%d\n",x,level);
		if(x==-1)return 0;
		if(level==-1)return 0;
		if(x==at[level])ans+=pat[level];
		else if(x<=at[level-1]+1)am(x-1,level-1);
		else if(x==at[level-1]+2)ans+=pat[level-1]+1;
		else {
				ans+=pat[level-1]+1;
				am(x-(at[level-1]+2),level-1);
		}
		return 0;
}

int main(){
		int n,i;
		long long x;
		scanf("%d%lld",&n,&x);
		for(i=1;i<=50;i++)at[i]=at[i-1]*2+3;
		for(i=1;i<=50;i++)pat[i]=pat[i-1]*2+1;
		am(x,n);
		printf("%lld\n",ans);
		return 0;
}