| Author: | ACM ICPC 2008-2009, NEERC, Northern Subregional Contest | Time limit: | 3 sec | |
| Input file: | fenwick.in | Memory limit: | 256 Mb | |
| Output file: | fenwick.out |
Fenwick tree is a data structure effectively supporting prefix sum queries.
For a number t denote as h(t) maximal k such that t is divisible by 2k. For example, h(24) = 3, h(5) = 0. Let l(t) = 2h(t), for example, l(24) = 8, l(5) = 1.
Consider array a[1], a[2], …, a[n] of integer numbers. Fenwick tree for this array is the array b[1], b[2], …, b[n] such that
b[i] = ∑ij = i − l(i) + 1a[j].
So
b[1] = a[1],
b[2] = a[1] + a[2],
b[3] = a[3],
b[4] = a[1] + a[2] + a[3] + a[4],
b[5] = a[5],
b[6] = a[5] + a[6],
...
For example, the Fenwick tree for the array
a = (3, − 1, 4, 1, − 5, 9)
is the array
b = (3, 2, 4, 7, − 5, 4).
Let us call an array self-fenwick if it coincides with its Fenwick tree. For example, the array above is not self-fenwick, but the array a = (0, − 1, 1, 1, 0, 9) is self-fenwick.
You are given an array a. You are allowed to change values of some elements without changing their order to get a new array a′ which must be self-fenwick. Find the way to do it by changing as few elements as possible.
The first line of the input file contains n — the number of elements in the array. The second line contains n integer numbers — the elements of the array.
Output n numbers — the elements of the array a′. If there are several solutions, output any one.
1 ≤ n ≤ 100000.
The elements of the input array do not exceed 109 by their absolute values.
| No. | Input file (fenwick.in) |
Output file (fenwick.out) |
|---|---|---|
| 1 | |
|