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: Wrong Answer)

import java.util.*;
public class Main {
	Scanner sc = new Scanner(System.in);
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		new Main().doIt();
	}
	void doIt() {
		solveD();
	}
	long [] h, all;
	long fd(int n, long x) {
		//System.out.println(n + " " + x);
		long ans = 0;
		if(n == 1) ans = 0L;
		else if(x <= 1) ans = 0L;
		else if(x <= 1L + h[n-1]) {
			ans = fd(n-1, x-1);
		}
		else if(x <= 2L + h[n-1]) {
			ans = 1L + all[n-1];
		}
		else if(x <= 2L + 2L * h[n-1]) {
			ans = 1L + all[n-1] + fd(n-1, x - (2L + h[n-1]));
			
		} else {
			ans = 1L + 2L * all[n-1];
			
		}
		
		return ans;
	}
	void solveD() {
		int N = sc.nextInt();
		long X = sc.nextLong();
		h = new long[N+1];
		all = new long[N+1];
		h[0] = 1; all[0] = 1;
		for(int i = 1; i <= N; i++) {
			h[i] = 2L * h[i-1] + 3L;
			all[i] = 2L * all[i-1] + 1L;
		}
		//System.out.println(Arrays.toString(all));
		//System.out.println(Arrays.toString(h));

		long ans = fd(N, X);
		System.out.println(ans);
	}
	void solveC() {
		int N = sc.nextInt();
		int K = sc.nextInt();
		long [] h = new long[N];
		for(int i = 0; i < N; i++) {
			h[i] = sc.nextLong();
		}
		Arrays.sort(h);
		long ans = Long.MAX_VALUE;
		for(int i = K-1; i < N; i++) {
			long d = h[i] - h[i-K+1];
			ans = Math.min(ans, d);
		}
		System.out.println(ans);
		
	}
	void solveA() {
		int N = sc.nextInt();
		String ans = "Christmas";
		for(int i = N; i < 25; i++) {
			ans += " Eve";
		}
		System.out.println(ans);
	}
	void solveB() {
		int N = sc.nextInt();
		int [] p = new int[N];
		for(int i = 0; i < N; i++) {
			p[i] = sc.nextInt();
		}
		Arrays.sort(p);
		int ans = 0;
		for(int i = 0; i < N-1; i++) {
			ans +=p[i];
		}
		ans += p[N-1]/2;
		System.out.println(ans);
		
	}
}