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 int[] 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 int[n];
		for (int i = 0; i < n; i++) {
			nums[i] = Integer.parseInt(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 int[n];
			for (int i = 0; i < n; i++) {
				nums[i] = Integer.parseInt(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[prev];
						prev = mps;
						mps = mps+(int)Math.pow(2,maxPossibleStep(mps));						
					}
				}
			}
			System.out.println(sum);
		}
	}

}
