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.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.StringTokenizer;

public class Main {
    Scanner in;
    PrintWriter out;

    void setIn(String fI) {

        try {
            in = new Scanner(new FileInputStream(new File(fI)));
        } catch (FileNotFoundException e) {
            throw new Error(e);
        }
    }

    void setIn() {
        in = new Scanner(System.in);
    }

    void setOut(String fO) {
        try {
            out = new PrintWriter(new FileWriter(fO));
        } catch (IOException e) {
            throw new Error(e);
        }
    }

    void setOut() {
        out = new PrintWriter(System.out);
    }

    class Scanner {
        StringTokenizer st;
        BufferedReader in;
        String del;

        Scanner(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
            st = null;
            del = " \t\n\r\f";
        }

        void setDelimiters(String del) {
            this.del = del;
        }

        String next() {
            if (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(nextLine(), del);
            }
            return st.nextToken();
        }

        String nextLine() {
            try {
                st = null;
                return in.readLine();
            } catch (IOException e) {
                throw new Error(e);
            }
        }

        boolean hasNext() {
            try {
                return in.ready() || (st != null && st.hasMoreTokens());
            } catch (IOException e) {
                throw new Error(e);
            }
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

        BigDecimal nextBigDecimal() {
            return new BigDecimal(next());
        }

        int[] nextIntArray(int len) {
            int[] a = new int[len];
            for (int i = 0; i < len; i++) {
                a[i] = nextInt();
            }
            return a;
        }
    }

    public static void main(String[] args) {
        new Main().run();
    }

    void run() {
        setIn();
        setOut();
        try {
            solve();
        } finally {
            out.close();
        }
    }

    class Point {
        int x;
        int y;

        Point(int X, int Y) {
            x = X;
            y = Y;
        }

        @Override
        public boolean equals(Object o) {
            Point p = (Point) o;
            return p.x == x && y == p.y;
        }

        @Override
        public int hashCode() {
            return 31 * x + y;
        }
    }

    int getPos(int i, int n) {
        int pow = 1;
        while (i + pow * 2 <= n)
            pow *= 2;
        return pow + i;
    }

    void solve() {
        int n = in.nextInt();
        int[] a = in.nextIntArray(n);
        long curAns = 0;
        for (int i = 0; i < n - 1; i++) {
            int pos = getPos(i + 1, n) - 1;
            curAns += a[i];
            a[pos] += a[i];
            out.println(curAns);
        }
    }
}