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.LinkedList;
import java.util.Scanner;

public class Main1 {

    static int n;
    static long[] nums;

    public static void ReadConsole() {

        Scanner in = new Scanner(System.in);

        n = Integer.parseInt(in.nextLine());
        String str = in.nextLine();
        String[] strs = str.split(" ");
        nums = new long[n];
        for (int i = 0; i < n; i++) {
            nums[i] = Long.parseLong(strs[i]);
        }
    }

    public static void ReadFile() {
        try {
            FileInputStream fstream = new FileInputStream("in.txt");

            DataInputStream in = new DataInputStream(fstream);
            BufferedReader br = new BufferedReader(new InputStreamReader(in));
            n = Integer.parseInt(br.readLine());
            String str = br.readLine();
            in.close();

            String[] strs = str.split(" ");
            nums = new long[n];
            for (int i = 0; i < n; i++) {
                nums[i] = Long.parseLong(strs[i]);
            }
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    /**
     * @param args
     */
    public LinkedList<Integer> GetPossibleMove(int forNum) {
        LinkedList<Integer> res = new LinkedList<Integer>();
        res.add(forNum + 1);
        int t2 = 1;
        while (true) {
            t2 *= 2;
            if (t2 < n)
                res.add(forNum + t2);
            else
                break;
        }
        return res;
    }

    public static int maxPossibleStep(int forNum) {
        return (int) (Math.log(n - forNum - 1) / Math.log(2));
    }

    public static void main(String[] args) {
        ReadConsole();
        //ReadFile();

        // for (int k = 1; k < n; k++) {
        /*
         * int sum = 0; int[] cnums = nums.clone();
         * 
         * for (int i = 0; i < k; i++) { sum += cnums[i]; int prev = i;
         * 
         * int mps = i+(int)Math.pow(2,maxPossibleStep(i)); while (true) { if
         * (mps >= k) { break; } else { cnums[mps] += cnums[i]; break; //prev =
         * mps; //mps = mps+(int)Math.pow(2,maxPossibleStep(mps)); } }
         */
        // }
        long[] cnums = nums.clone();

        for (int i = 0; i < n; i++) {
            int prev = i;

            int mps = i + (int) Math.pow(2, maxPossibleStep(i));
            while (true) {
                cnums[mps] += cnums[i];
                break;
                // prev = mps;
                // mps = mps+(int)Math.pow(2,maxPossibleStep(mps));

            }
            
            //System.out.println(sum);
        }
        
        long sum = 0;
        for (int i = 0; i < n - 1; i++) {
            sum += cnums[i];
            System.out.println(sum);
        
        }
    }

}
