The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.

The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.

One move is choosing an integer i (1 ≤ i ≤ n) such that ai > 0 and an integer t (t ≥ 0) such that i + 2t ≤ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).

You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 ≤ k < n).

Input

The first input line contains a single integer n. The second line contains n integers ai (0 ≤ ai ≤ 104), separated by single spaces.

The input limitations for getting 20 points are: 

  * 1 ≤ n ≤ 300



The input limitations for getting 50 points are: 

  * 1 ≤ n ≤ 2000



The input limitations for getting 100 points are: 

  * 1 ≤ n ≤ 105

Output

Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams, or the %I64d specifier.

Examples

Input

4
1 0 1 2


Output

1
1
3


Input

8
1 2 3 4 5 6 7 8


Output

1
3
6
10
16
24
40
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Erik Odenman
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		EducationalGame solver = new EducationalGame();
		solver.solve(1, in, out);
		out.close();
	}
}

class EducationalGame {
	public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n = in.getInt();
        long cnt = 0;
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.getInt();
        }
        int pow2 = 1;
        while (2*pow2 < n) pow2 *= 2;
        for (int i = 0; i < n - 1; i++) {
            cnt += a[i];
            while (i+pow2 >= n) pow2 /= 2;
            a[i+pow2] += a[i];
            a[i] = 0;
            out.println(cnt);
        }
	}
}

class InputReader {
    private BufferedReader in;
    private StringTokenizer st;
    String token;

    public InputReader(InputStream inStream) {
        in = new BufferedReader(new InputStreamReader(inStream));
    }

    public int getInt() {
        return Integer.parseInt(next());
    }

    public String next() {
        String res = peekToken();
        token = null;
        return res;
    }

    public String peekToken() {
        if (token != null) return token;
        while (st == null || !st.hasMoreTokens()) {
            String line = null;
            try {
                line = in.readLine();
            } catch (IOException e) {
                throw new RuntimeException("No more tokens was found");
            }
            if (line == null) return null;
            st = new StringTokenizer(line);
        }
        return token = st.nextToken();
    }

    }

class OutputWriter  {

    PrintWriter out;

    public OutputWriter(OutputStream outStream) {
        out = new PrintWriter(outStream);
    }

    public OutputWriter(Writer writer) {
        out = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0) out.print(' ');
            out.print(objects[i]);
        }
    }

    public void println(Object... objects) {
        print(objects);
        out.println();
    }

    public void close() {
        out.close();
    }
}

