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 Main {
	public static void main(String[] args){
		solution s = new solution();
		s.solve();
		s.close();
	}
}

interface IO{
	Scanner in = new Scanner(new BufferedInputStream(System.in));
	PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
}

class solution implements IO{
	
	final int MAXN = (int) 1e5+5;
	long []a = new long [MAXN];
	long []b = new long [MAXN];
	int []ind = new int [20];
	
	int findIndex(int x, int n){ // find the max power of 2 plus x while less than n
		for(int i = 0; i < 20; i++){
			if(x + ind[i+1] > n)
				return ind[i];
		}
		return 1;
	}
	
	void solve(){
		
		int n = in.nextInt();
		
		ind[0] = 1;
		for(int i = 1; i != 20; i++){
			ind[i] = ind[i - 1] * 2;
		}
		
		for(int i = 1; i <= n; i++){
			a[i] = in.nextLong();
		}
		
		for(int i = 1; i < n; i++){
			int index = findIndex(i,n);
			a[i+index] += a[i];
			b[i] = a[i];
			a[i] = 0;
		}
		
		for(int i = 2; i < n; i++){
			b[i] += b[i-1];
		}
		
		for(int i = 1; i < n; i++){
			out.println(b[i]);
		}
		
	}
	
	void close(){
		in.close();
		out.close();
	}
}
