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
/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
//package javaforces;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.StringTokenizer;

/**
 *
 * @author XPMUser
 */
public class JavaForces {

    StringTokenizer st;
    BufferedReader in;
    PrintWriter out;
    
    public static void main(String[] args) throws NumberFormatException, IOException{
        // TODO code application logic here
        JavaForces solver = new JavaForces();
        solver.open();
        solver.solve();
        solver.close();
        
    }
    
    public void solve() throws NumberFormatException, IOException
    {
        int n = nextInt();
        BigInteger[] a = new BigInteger[n];
        for(int i=0; i<n; i++)
	{
		a[i] = new BigInteger(nextToken());
	}
        int t = 0;
        n--;
	int step = 0;
	while( (1 << ++step) <= n)
	{
		t  = 1 << step;
	}
        BigInteger res = BigInteger.valueOf(0);
        for(int i=0; i< n; i++)
	{
		if(a[i].compareTo(BigInteger.valueOf(0)) == 0)
		{
                        out.println(res);
			continue;
		}
		if(i + t > n)
                {
                    t = (t >> 1);
                }
		a[i+t] = a[i+t].add(a[i]);
		res = res.add(a[i]);
		out.println(res);
	}
        
    }
    
    public void open() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
    }

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

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

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

    public double nextDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(nextToken());
    }
    
    public void close() {
        out.flush();
        out.close();
    }

}
