Codeforces712 D. Maxim and Array (贪心)

题目连接：http://codeforces.com/contest/721/problem/D

D. Maxim and Array

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Recently Maxim has found an array of n integers, needed by no one. He immediately come up with idea of changing it: he invented positive integer x and decided to add or subtract it from arbitrary array elements. Formally, by applying single operation Maxim chooses integer i (1 ≤ i ≤ n) and replaces the i-th element of array ai either with ai + x or with ai - x. Please note that the operation may be applied more than once to the same position.

Maxim is a curious minimalis, thus he wants to know what is the minimum value that the product of all array elements (i.e. ) can reach, if Maxim would apply no more than k operations to it. Please help him in that.

Input

The first line of the input contains three integers n, k and x (1 ≤ n, k ≤ 200 000, 1 ≤ x ≤ 109) — the number of elements in the array, the maximum number of operations and the number invented by Maxim, respectively.

The second line contains n integers a1, a2, ..., an () — the elements of the array found by Maxim.

Output

Print n integers b1, b2, ..., bn in the only line — the array elements after applying no more than k operations to the array. In particular,  should stay true for every 1 ≤ i ≤ n, but the product of all array elements should be minimum possible.

If there are multiple answers, print any of them.

Examples

input

5 3 15 4 3 5 2

output

5 4 3 5 -1 

input

5 3 15 4 3 5 5

output

5 4 0 5 5 

input

5 3 15 4 4 5 5

output

5 1 4 5 5 

input

3 2 75 4 2

output

5 11 -5 

题目大意：给出一个序列，一个数x，一次操作可以让序列里的数+x或这-x，最多操作k次，要求最后序列的数乘积最小。

解题思路：贪心。每次对绝对值最小的数进行操作，然后对其分类讨论。

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