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>
struct Node {
  Node(int v = 1e9) { min = v; }
  Node(Node l, Node r) { min = std::min(l.min, r.min); }
  int min;
};
template <class i_t, class e_t>
class SegmentTree {
 public:
  void init(std::vector<e_t> base) {
    n = base.size();
    tree.resize(2 * n);
    for (int i = 0; i < n; i++) {
      tree[i + n] = i_t(base[i]);
    }
    for (int i = n - 1; i > 0; i--) {
      tree[i] = i_t(tree[i + i], tree[i + i + 1]);
    }
  }
  i_t qry(int l, int r) {
    i_t lp, rp;
    for (l += n, r += n; l < r; l /= 2, r /= 2) {
      if (l & 1) lp = i_t(lp, tree[l++]);
      if (r & 1) rp = i_t(tree[--r], rp);
    }
    return i_t(lp, rp);
  }

 private:
  int n;
  std::vector<i_t> tree;
};
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(NULL);
  int n;
  std::cin >> n;
  std::vector<int> a(n);
  std::vector<int> dist(n, 0);
  for (int i = 0; i < n; i++) {
    std::cin >> a[i];
    dist[i] = dist[i / 2] + i % 2;
  }
  SegmentTree<Node, int> tree;
  tree.init(dist);
  std::vector<long long> ans(n + 1, 0);
  for (int i = 0; i + 1 < n; i++) {
    int l = 1, r = n - i;
    while (l < r) {
      int nl = l, nr = r - 1;
      int got = tree.qry(nl, r).min;
      ans[i + l - 1] += got * a[i];
      while (nl < nr) {
        int mid = (nl + nr + 1) / 2;
        if (tree.qry(mid, r).min > got) {
          nr = mid - 1;
        } else {
          nl = mid;
        }
      }
      ans[i + nl] -= got * a[i];
      l = nl + 1;
    }
  }
  for (int i = 1; i < n; i++) {
    ans[i] += ans[i - 1];
  }
  for (int i = 0; i + 1 < n; i++) {
    std::cout << ans[i] << std::endl;
  }
}
