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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

	import java.util.*;
	import java.util.Map.Entry;
	 
	 
	 class Main {
		 static int mod =  (int) (Math.pow(10,9)+7);
		 static List<ArrayList<Integer>>  list = new ArrayList<ArrayList<Integer>>();
	    public static void main(String[] args) {
	    	
	        Scanner sc = new Scanner(System.in);
	        int N = sc.nextInt();	
	        long X = sc.nextLong();
	        long[] lp = new long[N+1];
	        long[] lsum =new long[N+1];
	        lp[0]=1;lsum[0]=1;
	        for(int i=1;i<=N;i++) {
	        	lp[i]=2*lp[i-1]+1;
	        	lsum[i]=2*lsum[i-1]+3;
	        }
	        
	        boolean isEat=false;
	        int now =N;
	        long ans=0;
	        while(X>0) {
	        	if(now>=0&&X>=lsum[now]) {
	        		X=X-lsum[now];
	        		ans=ans+lp[now];
	        		if(X>0) {
	        			ans++;
	        			X--;
	        		}
	        	} else {
	        		X--;
	        		now--;
	        	}
	        }
	        System.out.println(ans);
	    }
	}