#D9989. Maxim and Array
Maxim and Array
Maxim and Array
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 1 5 4 3 5 2
Output
5 4 3 5 -1
Input
5 3 1 5 4 3 5 5
Output
5 4 0 5 5
Input
5 3 1 5 4 4 5 5
Output
5 1 4 5 5
Input
3 2 7 5 4 2
Output
5 11 -5
inputFormat
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.
outputFormat
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 1 5 4 3 5 2
Output
5 4 3 5 -1
Input
5 3 1 5 4 3 5 5
Output
5 4 0 5 5
Input
5 3 1 5 4 4 5 5
Output
5 1 4 5 5
Input
3 2 7 5 4 2
Output
5 11 -5
样例
3 2 7
5 4 2
5 11 -5