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.io.*;
import java.util.*;

import static java.lang.Math.abs;

public class Tests {

    private static FastScanner fastScanner;
    private static FastPrinter fastPrinter;

    public static void main(String[] args) throws IOException {

        boolean onlineJudge = System.getProperty("ONLINE_JUDGE") != null;

        fastScanner = onlineJudge ?
                new FastScanner(new InputStreamReader(System.in)) :
                new FastScanner(new FileReader("input.in"));
        fastPrinter = onlineJudge ?
                new FastPrinter(new OutputStreamWriter(System.out)) :
                new FastPrinter(new FileWriter("output.out"));

        Locale.setDefault(Locale.US);
        solve(args);

        fastScanner.close();
        fastPrinter.close();

    }

    public static void solve(String[] args) throws IOException {
        int n = fastScanner.nextInt();
        int k = fastScanner.nextInt();
        int x = fastScanner.nextInt();
        long[] a = new long[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = fastScanner.nextInt();
        }

        int zeroCnt = 0;
        for (int i = 0; i < a.length; i++) {
            if (a[i] == 0)
                zeroCnt++;
        }

        if (zeroCnt != 0) {
            if (k < zeroCnt) {
                fastPrinter.printArr(a);
                return;
            }

            int sign = sign(a);

            for (int i = 0; i < a.length; i++) {
                if (a[i] == 0) {
                    if (zeroCnt > 1) {
                        a[i] += x;
                        k--;
                        zeroCnt--;
                    } else {
                        a[i] -= x * sign;
                        k--;
                        zeroCnt--;
                    }
                }
            }
        }

        int sign = sign(a);
        if (sign > 0) {
            int posOfAbsMin = 0;
            for (int i = 1; i < a.length; i++)
                if (abs(a[i]) < abs(a[posOfAbsMin]))
                    posOfAbsMin = i;

            if (abs(a[posOfAbsMin]) == (long) x * k) {
                a[posOfAbsMin] = 0;
                fastPrinter.printArr(a);
                return;
            } else if ((long) ((double) abs(a[posOfAbsMin]) / x + 1) > k) {
                for (int i = 0; i < k; i++)
                    a[posOfAbsMin] += a[posOfAbsMin] > 0 ? -x : x;
                fastPrinter.printArr(a);
                return;
            } else {
                if (a[posOfAbsMin] < 0)
                    while (a[posOfAbsMin] <= 0) {
                        a[posOfAbsMin] += x;
                        k--;
                    }
                else
                    while (a[posOfAbsMin] >= 0) {
                        a[posOfAbsMin] -= x;
                        k--;
                    }
            }
        }

        toNegativeLow(a, k, x);
        fastPrinter.printArr(a);
    }

    private static void toNegativeLow(long[] a, int k, int x) {
        PriorityQueue<Pair> m = new PriorityQueue<>();
        for (int i = 0; i < a.length; i++) {
            m.add(new Pair(a[i], i));
        }

        while (k > 0) {
            Pair t = m.poll();
            t.a += x * sign(t.a);
            m.add(t);
            k--;
        }

        while (!m.isEmpty()) {
            Pair t = m.poll();
            a[t.b] = t.a;
        }
    }

    private static int sign(long x) {
        return x == 0 ? 0 : x > 0 ? 1 : -1;
    }

    private static int sign(long a[]) {
        int sign = 1;

        for (int i = 0; i < a.length; i++) {
            if (a[i] != 0)
                sign *= sign(a[i]);
        }

        return sign;
    }
}

class Pair implements Comparable<Pair> {
    long a;
    int b;

    public Pair(long a, int b) {
        this.a = a;
        this.b = b;
    }

    @Override
    public int compareTo(Pair o) {
        return abs(a) == abs(o.a) ? 0 : abs(a) > abs(o.a) ? 1 : -1;
    }
}

class FastScanner {

    private BufferedReader bufferedReader;
    private StringTokenizer stringTokenizer;

    public FastScanner(Reader reader) {
        bufferedReader = new BufferedReader(reader);
        stringTokenizer = new StringTokenizer("");
    }

    public String nextToken() throws IOException {
        if (!stringTokenizer.hasMoreTokens())
            stringTokenizer = new StringTokenizer(bufferedReader.readLine());

        return stringTokenizer.nextToken();
    }

    public String nextToken(String delim) throws IOException {
        if (!stringTokenizer.hasMoreTokens())
            stringTokenizer = new StringTokenizer(bufferedReader.readLine());

        return stringTokenizer.nextToken(delim);
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public String nextWord() throws IOException {
        return nextToken();
    }

    public void close() throws IOException {
        stringTokenizer = null;
        bufferedReader.close();
    }
}

class FastPrinter {

    private BufferedWriter bufferedWriter;
    private PrintWriter printWriter;

    public FastPrinter(Writer writer) {
        bufferedWriter = new BufferedWriter(writer);
        printWriter = new PrintWriter(bufferedWriter);
    }

    public void println() {
        printWriter.println();
    }

    public void println(int x) {
        printWriter.println(x);
    }

    public void println(long x) {
        printWriter.println(x);
    }

    public void println(double x) {
        printWriter.println(x);
    }

    public void println(char x) {
        printWriter.println(x);
    }

    public void println(String x) {
        printWriter.println(x);
    }

    public void print(int x) {
        printWriter.print(x);
    }

    public void print(long x) {
        printWriter.print(x);
    }

    public void print(double x) {
        printWriter.print(x);
    }

    public void printArr(long[] arr) {
        for (long elem : arr) {
            print(elem);
            print(' ');
        }
        print('\n');
    }

    public void print(char x) {
        printWriter.print(x);
    }

    public void print(String x) {
        printWriter.print(x);
    }

    public void printf(Locale locale, String format, Object... args) {
        printWriter.printf(locale, format, args);
    }

    public void printf(String format, Object... args) {
        printWriter.printf(format, args);
    }

    public void close() throws IOException {
        printWriter.flush();
        printWriter.close();
        bufferedWriter.close();
    }
}