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;
inline long long get_num(char ch) {
  if (ch == '-')
    return 0;
  else if (ch >= 'a' && ch <= 'z') {
    return 1 + (ch - 'a');
  } else if (ch >= 'A' && ch <= 'Z') {
    return 27 + (ch - 'A');
  } else if (ch >= '0' && ch <= '9') {
    return 53 + (ch - '0');
  }
}
int dx[] = {1, 0, -1, 0}, dy[] = {0, 1, 0, -1};
inline int GA(long long n, vector<long long>& vec) {
  for (long long i = 0; i < n; ++i) {
    long long x;
    cin >> x;
    vec.push_back(x);
  }
  return 0;
}
inline int GAEG(long long m, vector<long long> vec[]) {
  for (long long i = 0; i < m; ++i) {
    long long x, y;
    cin >> x >> y;
    x--, y--;
    vec[x].push_back(y);
    vec[y].push_back(x);
  }
  return 0;
}
long long pw(long long x, long long y) {
  if (y == 0) return 1;
  long long o = y / 2;
  long long f = pw(x, o);
  if (y % 2) {
    return f * f * x;
  } else
    return f * f;
}
const long long MD = 1e9 + 7;
using namespace std;
int main() {
  long long o = 0;
  long long n;
  cin >> n;
  vector<long long> v;
  for (long long i = 0; i < n; ++i) {
    long long x;
    cin >> x;
    v.push_back(x);
  }
  vector<long long> ans;
  for (long long i = 0; i < n - 1; ++i) {
    if (v[i]) {
      long long p;
      bool bl = false;
      for (int j = 20; j >= 0; j--) {
        p = i + pw(2, j);
        if (p < n) break;
      }
      if (p < n) {
        v[p] += v[i];
        o += v[i];
      }
    }
    ans.push_back(o);
  }
  for (auto i : ans) cout << i << endl;
  return 0;
}
