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).
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:
The input limitations for getting 50 points are:
The input limitations for getting 100 points are:
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 C++. It is preferred to use the cin, cout streams, or the %I64d specifier.
4
1 0 1 2
1
1
3
8
1 2 3 4 5 6 7 8
1
3
6
10
16
24
40