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).
