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
#include <string>
#include <vector>
#include <iostream>
#include <sstream>
#include <queue>
#include <fstream>
#include <set>
#include <map>
#include <vector>
#include <bitset>
#include <algorithm>
#include <functional>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <utility>

using namespace std;

#define SIZE(X) ((int)X.size())
#define LENGTH(X) ((int)X.length())
#define MP(A,B) make_pair(A,B)
typedef long long int64;
typedef unsigned long long uint64;
#define two(X) (1<<(X))
#define twoL(X) (((int64)(1))<<(X))
#define contain(S,X) ((S&two(X))>0)
#define containL(S,X) ((S&twoL(X))>0)
const double pi=acos(-1.0);
const double eps=1e-11;
template<class T> void checkmin(T &a,T b){if (b<a) a=b;}
template<class T> void checkmax(T &a,T b){if (b>a) a=b;}
template<class T> T sqr(T x) {return x*x;}
int countbit(int n) {return (n==0)?0:(1+countbit(n&(n-1)));}
int lowbit(int n) {return (n^(n-1))&n;}
typedef pair<int,int> ipair;
template<class T> void out(T A[],int n) { for (int i=0;i<n;i++) cout<<A[i]<<" ";cout<<endl;}
template<class T> void out(vector<T> A,int n=-1) {  if (n==-1) n=A.size();  for (int i=0;i<n;i++) cout<<A[i]<<" ";  cout<<endl;}
template<class T> T gcd(T a,T b){  if (a<0) return gcd(-a,b);  if (b<0) return gcd(a,-b);  return (b==0)?a:gcd(b,a%b);}
template<class T> T lcm(T a,T b){  return a*(b/gcd(a,b));}
int64 toInt64(string s){  istringstream sin(s);  int64 t;  sin>>t;  return t;}
int64 toInt(string s){  istringstream sin(s);  int t;  sin>>t;  return t;}
string toString(int64 v){  ostringstream sout;  sout<<v;  return sout.str();}
string toString(int v){  ostringstream sout;  sout<<v;  return sout.str();}

__int64 bin[100];
__int64 dd[100004];
__int64 dp[100004];
int n;
void init(){
	bin[0] = 1;
	for (int i = 1; i <= 30; i++)
	{
		bin[i] = bin[i-1]*2;
	}
}

void work(){
	__int64 v1,cnt;
	int pos;
	dp[0] = 0;
	for (int i = 0; i < n - 1; i++)
	{
		if ( dd[i] == 0)
		{
			dp[i+1] = dp[i];
			continue;
		}
		else {
			v1 = dd[i];
			cnt = n - i - 1;
			pos = lower_bound(bin,bin+30,cnt) - bin;
			
			if (pos != 0 && bin[pos] > cnt)
			{
				pos--;
			}
		//	cout<<"pos "<<pos<<endl;
			dd[i + bin[pos]] += dd[i];

			dp[i+1] = dp[i] + v1;
		}
	}
	for (int i = 1; i < n; i++)
	{
		printf("%d\n",dp[i]);
	}
}

int main(){
	//	freopen("d:/1.in","r",stdin);
	init();
	while (scanf("%d",&n) != EOF)
	{
		for (int i = 0; i < n; i++)
		{
			scanf("%d",dd+i);
		}
		work();
	}
	return 0;
}