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>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
const double pi = acos(-1.0);
const double eps = 1e-11;
const int p = 1000000007;
int countbit(int n) { return n == 0 ? 0 : countbit(n / 2) + n % 2; }
int lowbit(int n) { return (n ^ (n - 1)) & n; }
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
long long lcm(long long a, long long b) { return a * b / gcd(a, b); }
long long toInt64(string s) {
  istringstream sin(s);
  long long t;
  sin >> t;
  return t;
}
template <typename T>
T sqr(T n) {
  return n * n;
}
template <typename T>
void out(T& v) {
  for (int i = 0; i < v.size(); i++) cout << v[i] << ' ';
  cout << endl;
}
class Timer {
 public:
  double start;
  Timer() { start = static_cast<double>(clock()); }
  void out() { cout << "TIME: " << (clock() - start) / CLOCKS_PER_SEC << endl; }
};
void solve() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  int m = 1 << 20;
  int r = 0;
  for (int i = 0; i < n - 1; i++) {
    r += a[i];
    cout << r << (i == n - 2 ? '\n' : ' ');
    while (i + m >= n) m >>= 1;
    a[i + m] += a[i];
  }
}
int main() {
  Timer timer;
  cout.sync_with_stdio(false);
  cin.sync_with_stdio(false);
  solve();
  return EXIT_SUCCESS;
}
