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.*;
import java.util.*;

public class TaskA {
    BufferedReader br;
    PrintWriter out;
    StringTokenizer stok;

    String nextToken() throws IOException {
        while (stok == null || !stok.hasMoreTokens()) {
            String s = br.readLine();
            if (s == null) {
                return null;
            }
            stok = new StringTokenizer(s);
        }
        return stok.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());
    }

    char nextChar() throws IOException {
        return (char) (br.read());
    }

    String nextLine() throws IOException {
        return br.readLine();
    }

    void solve() throws IOException {
        int n = nextInt();
        int[] a = new int[n];
        long ans = 0;
        a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] += nextInt();
            int cur = 1;
            while (i + cur * 2 < n) {
                cur *= 2;
            }
            if (i == n - 1) {
                break;
            }
            ans += (long) a[i];
            out.println(ans);
            a[i + cur] += a[i];
        }
    }

    void run() throws IOException {
        // br = new BufferedReader(new FileReader("input.txt"));
        // out = new PrintWriter("output.txt");
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        br.close();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        // Locale.setDefault(Locale.US);
        new TaskA().run();
    }
}