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 Solution {


	private StringTokenizer st;
	private BufferedReader in;
	private PrintWriter out;

	int[] a;
	int[] d;
	
	long dfs(int i, int last, int dd) {
		if (dd >= d[i]) {
			return 0;
		}
		long ret = (long)(d[i] - dd) * a[i];
		d[i] = dd;
		for (int j = 1; j <= i && j < last; j *= 2) {
			ret += dfs(i - j, j, dd + 1);
		}
		return ret;
	}

	public void solve() throws IOException {
		int n = nextInt();
		a = new int[n];
		d = new int[n];
		for (int i = 0; i < n; ++i) {
			a[i] = nextInt();
		}
		Arrays.fill(d, 1000000000);
		d[n - 1] = 0;
		long[] ans = new long[n];
		for (int i = n - 1; i >= 0; --i) {
			for (int j = 1; j <= i; j *= 2) {
				d[i - j] = Math.min(d[i - j], d[i] + 1);
			}
			ans[n - 1] += (long)a[i] * d[i]; 
		}
		for (int t = n - 2; t > 0; --t) {
			ans[t] = ans[t + 1] - dfs(t, t + 1, 0);
		}
		for (int i = 1; i < n; ++i) {
			out.println(ans[i]);
		}
	}

	public void run() throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		eat("");
		
		solve();
		
		out.close();
	}
	
	void eat(String s) {
		st = new StringTokenizer(s);
	}
	
	String next() throws IOException {
		while (!st.hasMoreTokens()) {
			String line = in.readLine();
			if (line == null) {
				return null;
			}
			eat(line);
		}
		return st.nextToken();
	}
	
	int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	
	long nextLong() throws IOException {
		return Long.parseLong(next());
	}
	
	double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
	
	static boolean failed = false;
	
	public static void main(String[] args) throws IOException {
		Locale.setDefault(Locale.US);
		new Solution().run();
	}
	
}