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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.lang.Character;
import java.lang.Long;
import java.lang.Math;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;
import java.util.Arrays;

public class TaskC {
	BufferedReader reader;
	StringTokenizer tokenizer = new StringTokenizer("");

	public static void main(String[] args) throws IOException {
		new TaskC().run();
	}

	private void run() throws IOException {
		tokenizer = null;
		reader = new BufferedReader(new InputStreamReader(System.in));
		solve();
	}

	public static int divide_by_two(int x, int y){

		if (y == 0) return 0;
	
		x = x - y;
		int r = 1;
		int c = 0;
		while(x != 0){
			r = x % 2;
			x = (int)(x / 2);	
			if (r == 1) c++;
		}
		return c;
	}

	private void solve() throws IOException {
		int N = nextInt();
		List<Integer> A = new ArrayList<Integer>();
		List<Integer> dp = new ArrayList<Integer>();
		List<Integer> ans = new ArrayList<Integer>();
		for (int i = 0; i < 301; i++) {
			A.add(0);
		}
		for (int i = 0; i < N + 1; i++) {
			dp.add(0);
			ans.add(0);
		}
		for (int i = 1; i <= N; i++) A.set(i,nextInt());

		for (int k = N - 1; k >= 1; k--) {
			int sum = 0;
			for (int index = 1; index <= k; index++) {
				int min = Integer.MAX_VALUE;
				int temp = 0;
				for (int n = N; n >= k + 1; n--) {
					if (dp.get(index) > n) {
						min = 1;
						sum += A.get(index);
					break;
				} else {
					temp = divide_by_two(n, index);
					min = Math.min(min, temp);
					if (min == 1) {
						sum += A.get(index);
						dp.set(index, n);
						break;
					}
				}
			}
			if (min != 1) sum += A.get(index) * min;
		}
		ans.set(k, sum);
	}
	
		for (int i = 1; i <= N - 1; i++) {
			System.out.print(ans.get(i));
			if (i != N - 1) System.out.print("\n");
		}
	}
	
	String nextToken() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens())
			tokenizer = new StringTokenizer(reader.readLine());
		return tokenizer.nextToken();
	}

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

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