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. <image>) 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 (<image>) — 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, <image> 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 
import java.util.*;

/**
 * Class description...
 * Created by Harrison Fang on September 30, 2016.
 */
public class MaximAndArray {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt(), k = in.nextInt(), x = in.nextInt();

        int negs = 0;
        ArrayList<Integer> zeros = new ArrayList<>();

        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            int a = in.nextInt();
            arr[i] = a;

            if (a == 0) {
                zeros.add(i);
            }
            else if (a < 0) negs++;
        }

        if (zeros.size() > 0) {
            if (negs % 2 == 0) {
                if (zeros.size() % 2 == 0) {
                    arr[zeros.get(0)] -= x; k--; negs++;
                    for (int i = 1; i < zeros.size() && k > 0; i++) {
                        arr[zeros.get(i)] += x; k--;
                    }
                } else {
                    for (int i = 0; i < zeros.size() && k > 0; i++) {
                        arr[zeros.get(i)] -= x; k--; negs++;
                    }
                }
            } else {
                if (zeros.size() % 2 == 0) {
                    for (int i = 0; i < zeros.size() && k > 0; i++) {
                        arr[zeros.get(i)] -= x; k--; negs++;
                    }
                } else {
                    for (int i = 0; i < zeros.size() && k > 0; i++) {
                        arr[zeros.get(i)] += x; k--;
                    }
                }
            }
        }

        if (k > 0) {
            if (negs % 2 == 0) {
                int pos = -1;
                long min = Integer.MAX_VALUE;
                for (int i = 0; i < n; i++) {
                    long val = Math.abs(arr[i]);
                    if (val < min) {
                        pos = i;
                        min = val;
                    }
                }
                long num = arr[pos];
                if (num > 0) {
                    while (num >= 0 && k > 0) {
                        num -= x;
                        k--;
                    }
                } else {
                    while (num <= 0 && k > 0) {
                        num += x;
                        k--;
                    }
                }
                arr[pos] = num;
            }

            PriorityQueue<Pair> pq = new PriorityQueue<>(new Comparator<Pair>() {
                @Override
                public int compare(Pair o1, Pair o2) {
                    return Long.compare(Math.abs(o1.val), Math.abs(o2.val));
                }
            });
            for (int i = 0; i < n; i++) {
                pq.offer(new Pair(i, arr[i]));
            }

            while (k > 0) {
                Pair p = pq.poll();
//                System.err.println(p.pos);
                if (p.val > 0) {
                    p.val += x;
                    arr[p.pos] += x;
                } else {
                    p.val -= x;
                    arr[p.pos] -= x;
                }
                k--;

                pq.offer(p);
            }
        }

        StringBuilder sb = new StringBuilder();
        for (long a : arr) {
            sb.append(a).append(' ');
        }
        sb.deleteCharAt(sb.length() - 1);
        System.out.println(sb.toString());
    }

    static class Pair {
        int pos; long val;
        Pair(int pos, long val) { this.pos = pos; this.val = val; }
    }
}