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 javafx.util.Pair;

import java.io.*;
import java.util.Comparator;
import java.util.StringTokenizer;
import java.util.TreeSet;

/**
 * @author Aydar Gizatullin a.k.a. lightning95, aydar.gizatullin@gmail.com
 *         Created on 10/17/16.
 */

public class ProbD {
    private void solve() {
        int n = rw.nextInt();
        int k = rw.nextInt();
        int x = rw.nextInt();
        long[] a = new long[n];
        TreeSet<Pair<Long, Integer>> set = new TreeSet<>((Comparator<Pair<Long, Integer>>)
                (p, t) -> {
                    int c = Long.compare(Math.abs(p.getKey()), Math.abs(t.getKey()));

                    return c == 0 ? Integer.compare(p.getValue(), t.getValue()) : c;
                });

        int less = 0;
        int numz = 0;
        int high = 0;
        for (int i = 0; i < n; ++i) {
            a[i] = rw.nextInt();
            set.add(new Pair<>(a[i], i));
            less += a[i] < 0 ? 1 : 0;
            high += a[i] > 0 ? 1 : 0;
            numz += a[i] == 0 ? 1 : 0;
        }
        if (numz > k) {
            for (long t : a) {
                rw.print(t + " ");
            }
            rw.println();
            return;
        }
        for (; k > 0 && numz > 0; --k) {
            Pair<Long, Integer> p = set.pollFirst();
            long v;
            int id = p.getValue();

            if (less % 2 == 1) {
                v = x;
                --numz;
                high++;
            } else {
                v = -x;
                --numz;
                less++;
            }
            a[id] = v;
            set.add(new Pair<>(v, id));
        }

        if (less % 2 == 0) {
            Pair<Long, Integer> p = set.pollFirst();
            long v = p.getKey();
            int id = p.getValue();
/*            if (Math.abs(v) / x + (Math.abs(v) % x != 0 ? 1 : 0) > k) {
                return;
            }*/

            boolean to = v >= 0;
            for (; k > 0; ) {
                if (to) {
                    v -= x;
                    --k;
                    if (v < 0) break;
                }else {
                    v += x;
                    --k;
                    if (v > 0) break;
                }
            }
            a[id] = v;
            set.add(new Pair<>(v, id));
        }

        for (int i = 0; i < k; ++i) {
            Pair<Long, Integer> p = set.pollFirst();
            long v = p.getKey();
            int id = p.getValue();
            if (v >= 0) {
                v += x;
            } else {
                v -= x;
            }
            a[id] = v;
            set.add(new Pair<>(v, id));
        }

        for (long l : a) {
            rw.print(l + " ");
        }
        rw.println();
    }

    private RW rw;
    private String FILE_NAME = "file";

    public static void main(String[] args) {
        new ProbD().run();
    }

    private void run() {
        rw = new RW(FILE_NAME + ".in", FILE_NAME + ".out");
        solve();
        rw.close();
    }

    private class RW {
        private StringTokenizer st;
        private PrintWriter out;
        private BufferedReader br;
        private boolean eof;

        RW(String inputFile, String outputFile) {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));

            File f = new File(inputFile);
            if (f.exists() && f.canRead()) {
                try {
                    br = new BufferedReader(new FileReader(inputFile));
                    out = new PrintWriter(new FileWriter(outputFile));
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
        }

        private String nextLine() {
            String s = "";
            try {
                s = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }

        private String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    eof = true;
                    return "-1";
                }
            }
            return st.nextToken();
        }

        private long nextLong() {
            return Long.parseLong(next());
        }

        private int nextInt() {
            return Integer.parseInt(next());
        }

        private void println() {
            out.println();
        }

        private void println(Object o) {
            out.println(o);
        }

        private void print(Object o) {
            out.print(o);
        }

        private void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
            out.close();
        }
    }
}

