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.*;

public class A2{
	public static void main(String ar[]){
		try{
			BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
			int n=Integer.parseInt(in.readLine());
			String s=in.readLine();
			int a[]=new int[n+1];
			int i=1;
			for(int j=0;j<s.length();j++){
				char c=s.charAt(j);
				if(c==' ')i++;
				else a[i]=a[i]*10+(c-'0');
			}
			//for(int j=1;j<n+1;j++)System.out.println(a[j]);
			int r[]=new int[n];
			for(int j=1;j<n;j++){
				int aj=a[j];
				if(aj==0){r[j]=r[j-1];continue;}
				int z=n-j;
				int b=0;
				while(z!=1){z>>=1;b++;}
				r[j]=aj+r[j-1];
				a[j+(1<<b)]+=aj;
			}
			//System.out.println("--");
			//for(int j=1;j<n+1;j++)System.out.println(a[j]);
			//System.out.println("--");
			for(int j=1;j<n;j++)System.out.println(r[j]);
		}catch(Exception e){}
	}
}