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;
const int maxn = 220000, maxlen = 502 * 502 + 20, consta = 1050,
          maxi = consta + 4, big = 10000000, magic = 239, magic1 = 359;
const long long INF = 1000000000;
const char BLANK = '-', FULL = '#';
string s;
char aa;
long double p[maxn];
set<pair<int, int> > low;
int a[maxn], dp[maxn];
int dps[maxn][23];
int main() {
  int n;
  cin >> n;
  long long sum = 0;
  for (int i = 0; i < n; ++i) {
    scanf("%d", &a[i]);
    sum += a[i];
  }
  for (int i = 1; i <= n; ++i) {
    int sm = 0;
    for (int j = 25; j >= 0; --j) {
      if ((1 << j) & i) ++sm;
      dps[i][sm] = (i >> j) << j;
    }
    for (; sm < 22; ++sm) dps[i][sm + 1] = dps[i][sm];
  }
  long long res = 0;
  dp[0] = 1;
  int wha = 0;
  while ((1 << (wha + 1)) < n) ++wha;
  low.insert(make_pair(1 << wha, 0));
  for (int i = 1; i < n; ++i) low.insert(make_pair(i, i));
  if (sum == 0) {
    for (int i = 0; i < n; ++i) printf("0\n");
    return 0;
  }
  cout << a[0] * 1 << endl;
  res = a[0] * 1;
  for (int h = 1; h + 1 < n; ++h) {
    while (low.begin()->first <= h) {
      int who = low.begin()->second;
      low.erase(low.begin());
      res -= dp[who] * a[who];
      ++dp[who];
      res += dp[who] * a[who];
      low.insert(make_pair(dps[n - who - 1][dp[who]] + who, who));
    }
    printf("%I64d\n", res);
  }
}
