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 <bits/stdc++.h>
using namespace std;
class comp {
 public:
  bool operator()(const pair<long long int, long long int>& lhs,
                  const pair<long long int, long long int>& rhs) const {
    if (lhs.first > rhs.first)
      return 1;
    else if (lhs.first == rhs.first && lhs.second > rhs.second)
      return 1;
    return 0;
  }
};
int main() {
  long long int n;
  long long int count;
  cin >> n;
  vector<long long int> ip(n);
  vector<long long int> power2;
  for (long long int i = 0; pow(2, i) <= 2000; i++) power2.push_back(pow(2, i));
  vector<priority_queue<pair<long long int, long long int>,
                        vector<pair<long long int, long long int> >, comp> >
      vpq(n);
  for (long long int i = 1; i <= n; i++) {
    queue<pair<long long int, long long int> > bfs;
    vector<bool> vis(n);
    bfs.push(make_pair(i, 0));
    while (!bfs.empty()) {
      pair<long long int, long long int> temp = bfs.front();
      bfs.pop();
      if (vis[temp.first - 1] == 1) continue;
      vis[temp.first - 1] = 1;
      if (temp.first != i)
        vpq[i - 1].push(make_pair(temp.second, temp.first - 1));
      long long int lim = 0;
      while (power2[lim] + temp.first <= n) {
        bfs.push(make_pair(power2[lim] + temp.first, temp.second + 1));
        lim++;
      }
    }
  }
  for (long long int i = 0; i < n; i++) {
    cin >> ip[i];
  }
  for (long long int i = 1; i < n; i++) {
    count = 0;
    for (long long int j = 0; j < i; j++) {
      pair<long long int, long long int> temp = vpq[j].top();
      while (temp.second < i && !vpq[j].empty()) {
        vpq[j].pop();
        temp = vpq[j].top();
      }
      count += (long long int)(temp.first * ip[j]);
    }
    cout << count << "\n";
  }
  return 0;
}
