A8517 | Educational Game

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 $a_{i}$ numbered from $1$ to $n$ . The goal of the game is to make numbers $a_{1},a_{2},...,a_{k}$ (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 $a_{i}>0$ and an integer $t$ $(t>=0)$ such that $i+2^{t}<=n$ . After the values of $i$ and $t$ have been selected, the value of $a_{i}$ is decreased by $1$ , and the value of $a_{i+2^{t}}$ 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 $a_{i}$ . 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 $k$ $(1<=k<n)$ .

The first input line contains a single integer $n$ . The second line contains $n$ integers $a_{i}$ ( $0<=a_{i}<=10^{4}$ ), 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:

- $1<=n<=10^{5}$

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 $a_{i}$ 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.