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 A {

	final int MOD = 1000000007;
	final double eps = 1e-12;

	public A () throws IOException {
		int N = sc.nextInt();
		long [] A = sc.nextLongs();
		
		start();
		
		long res = 0;
		for (int k = 0; k < N-1; ++k) {
			int t = 0;
			while ((k+1) + (1 << t) <= N) ++t;
			--t;
			A[k + (1 << t)] += A[k];
			res += A[k];
			print(res);
		}
	}

	////////////////////////////////////////////////////////////////////////////////////
	
	static MyScanner sc;
	static PrintWriter pw = new PrintWriter(System.out);
	
	static void print (Object... a) {
		StringBuffer b = new StringBuffer();
		for (Object o : a)
			b.append(" ").append(o);
		pw.println(b.toString().trim());
	}

	static void exit (Object... a) {
		print(a);
		exit();
	}

	static void exit () {
		pw.flush();
		System.err.println("------------------");
		System.err.println("Time: " + (millis() - t) / 1000.0);
		System.exit(0);
	}
	
	static class MyScanner {
		String next() throws IOException {
			newLine();
			return line[index++];
		}
		
		char [] nextChars() throws IOException {
			return next().toCharArray();
		}
		
		double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
		
		int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		
		long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		
		String nextLine() throws IOException {
			line = null;
			return r.readLine();
		}
		
		String [] nextStrings() throws IOException {
			line = null;
			return r.readLine().split(" ");
		}
		
		int [] nextInts() throws IOException {
			String [] L = nextStrings();
			int [] res = new int [L.length];
			for (int i = 0; i < L.length; ++i)
				res[i] = Integer.parseInt(L[i]);
			return res;
		}
		
		long [] nextLongs() throws IOException {
			String [] L = nextStrings();
			long [] res = new long [L.length];
			for (int i = 0; i < L.length; ++i)
				res[i] = Long.parseLong(L[i]);
			return res;
		}

		boolean eol() {
			return index == line.length;
		}

		//////////////////////////////////////////////
		
		private final BufferedReader r;

		MyScanner () throws IOException {
			this(new BufferedReader(new InputStreamReader(System.in)));
		}
		
		MyScanner(BufferedReader r) throws IOException { 
			this.r = r;
		}
		
		private String [] line;
		private int index;

		private void newLine() throws IOException {
			if (line == null || eol()) {
				line = r.readLine().split(" ");
				index = 0;
			}
		}		
	}
	
	////////////////////////////////////////////////////////////////////////////////////
	
	public static void main(String[] args) throws IOException {
		run();
		exit();
	}

	static void start() {
		t = millis();
	}

	static void run () throws IOException {
		sc = new MyScanner ();
		new A();
	}

	static long t;
	
	static long millis() {
		return System.currentTimeMillis();
	}	
}
