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
/**
 * Created with IntelliJ IDEA.
 * User: Zakhar_Voit
 * Date: 28.04.12
 * Time: 22:10
 */

import java.io.*;
import java.util.*;

import static java.lang.System.exit;

public class A {
    BufferedReader in;
    PrintWriter out;
    StringTokenizer st = new StringTokenizer("");

    int n;
    int[] a, d;

    void init() {

    }

    void read() throws IOException {
        n = nextInt();
        a = new int[n];
        d = new int[n - 1];
        for (int i = 0; i < n; i++) a[i] = nextInt();
    }

    void solve() {
        for (int k = 0; k < n - 1; k++) {
            int off = 0;
            while (k + (1 << (off + 1)) < n) off++;

            d[k] = (k > 0 ? d[k - 1] : 0) + a[k];
            a[k + (1 << off)] += a[k];
            a[k] = 0;
        }
    }

    void write() {
        for (int i = 0; i < n - 1; i++) out.println(d[i]);
    }

    public void run() throws IOException {
        openIO();
        init();
        read();
        solve();
        write();
        out.close();
    }

    static public void main(String[] args) throws IOException {
        new Thread(null, new Runnable() {
            public void run() {
                try {
                    new A().run();
                } catch (Throwable e) {
                    e.printStackTrace();
                    exit(999);
                }
            }
        }, "1", 1 << 23).start();
    }

    public void openIO() throws IOException {
        if (new File("input.txt").exists()) {
            System.setIn(new FileInputStream("input.txt"));
            out = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
        } else {
            out = new PrintWriter(System.out);
        }
        in = new BufferedReader(new InputStreamReader(System.in));
    }

    String nextToken() throws IOException {
        while (!st.hasMoreTokens())
            st = new StringTokenizer(in.readLine());
        return st.nextToken();
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    String nextLine() throws IOException {
        st = new StringTokenizer("");
        return in.readLine();
    }

    boolean EOF() throws IOException {
        while (!st.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null)
                return true;
            st = new StringTokenizer(s);
        }
        return false;
    }
}