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.util.*;

/*
 *	
 *	A.java
 *	Written by Andy Huang: 8:19:51 AM Apr 28, 2012
 */
public class A {
	static final int twoe[] = {1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536};
	static boolean toend[];
	
	static void solve() {
		int n = in.nInt();
		long a[] = new long[n];
		toend = new boolean[n];
		for (int i = 0; i < n; i++){
			a[i] = in.nLong();
			for (int x : twoe){
				if (i + x == n-1)
					toend[i] = true;
			}
		}
		long dp[] = new long[n - 1];
		for (int i = 0; i < n - 1; i++){
			if (a[i] == 0)
				continue;
			if (toend[i]){
				dp[i] = a[i];
				a[i] = 0;
				continue;
			}
			for (int j = 16; j >= 0; j--){
				if (i + twoe[j] < n){
					dp[i] = a[i];
					a[i + twoe[j]] += a[i];
					a[i] = 0;
					break;
				}
			}
		}
		long sum = 0;
		for (long ans : dp){
			sum += ans;
			out.appendln(sum);
		}
	}

	public static void main(String[] args) {
		in = new Input();
		out = new Output();
		solve();
		out.print();
	}

	static Output out;
	static Input in;

	static void pln(Object o) {
		System.out.println(o);
	}

	static void pf(Object o) {
		System.out.print(o);
	}

}

final class Input {
	private java.io.BufferedReader reader;
	private java.util.StringTokenizer tokenizer;

	public Input() {
		reader = new java.io.BufferedReader(new java.io.InputStreamReader(System.in));
		tokenizer = null;
	}

	public String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new java.util.StringTokenizer(reader.readLine());
			}
			catch (java.io.IOException e) {
				throw new RuntimeException("Input Error");
			}
		}
		return tokenizer.nextToken();
	}

	public String nLine() {
		try {
			return reader.readLine();
		}
		catch (java.io.IOException e) {
			throw new RuntimeException(e);
		}
	}

	public long nLong() {
		return Long.parseLong(next());
	}

	public int nInt() {
		return Integer.parseInt(next());
	}

	public double nDouble() {
		return Double.parseDouble(next());
	}

}

final class Output {
	public StringBuilder buffer;

	Output() {
		buffer = new StringBuilder();
	}

	Output(int size) {
		buffer = new StringBuilder(size);
	}

	void print() {
		System.out.print(buffer.toString());
	}

	void flush() {
		System.out.flush();
	}

	<T> void append(T obj) {
		buffer.append(obj);
	}

	<T> void appendln(T obj) {
		append(obj);
		append('\n');
	}

	void delete(int index) {
		buffer.deleteCharAt(index);
	}

}