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.