Educational Game

2000ms

262144K

Description:

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 a₁, a₂, ..., 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).

Input:

The first input line contains a single integer n. The second line contains n integers a_i (0 ≤ a_i ≤ 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 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.

Sample Input:

4
1 0 1 2

Sample Output:

1
1
3

Sample Input:

8
1 2 3 4 5 6 7 8

Sample Output:

Informação

Provedor Codeforces

Código CF178A1