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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.PriorityQueue;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Queue;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Rustam Musin (PloadyFree@gmail.com)
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        private int n;
        private int k;
        private long x;
        private long[] a;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            n = in.readInt();
            k = in.readInt();
            x = in.readLong();
            a = IOUtils.readLongArray(in, n);
            solve();
            out.print(a);
        }

        private void solve() {
            boolean negative = isNegative(a);
            for (int i = 0; i < n; i++) {
                if (k > 0 && a[i] == 0) {
                    a[i] = negative ? x : -x;
                    k--;
                    negative = true;
                }
            }
            if (k == 0) {
                return;
            }

            if (!negative) {
                int minByModPosition = minByModPosition(a);
                int oldSign = sign(a[minByModPosition]);
                if (x * k >= Math.abs(a[minByModPosition])) {
                    while (true) {
                        if (k == 0) {
                            break;
                        }
                        int curSign = sign(a[minByModPosition]);
                        if (curSign == 0 || curSign == oldSign) {
                            a[minByModPosition] -= x * oldSign;
                            k--;
                        } else {
                            break;
                        }
                    }
                } else {
                    while (k-- > 0) {
                        a[minByModPosition] -= x * oldSign;
                    }
                    return;
                }
            }
            if (k == 0) {
                return;
            }

            Queue<Integer> q = new PriorityQueue<>(Comparator.comparing(i -> Math.abs(a[i])));
            for (int i = 0; i < n; i++) {
                q.add(i);
            }
            while (k > 0) {
                int idx = q.poll();
                a[idx] += x * sign(a[idx]);
                q.add(idx);
                k--;
            }
        }

        private boolean isNegative(long[] a) {
            int cnt = 0;
            for (long i : a) {
                if (i < 0) {
                    cnt++;
                }
            }
            return cnt % 2 == 1;
        }

        private int sign(long n) {
            return n < 0 ? -1 : n > 0 ? 1 : 0;
        }

        private int minByModPosition(long[] a) {
            int pos = 0;
            for (int i = 0; i < a.length; i++) {
                if (Math.abs(a[i]) < Math.abs(a[pos])) {
                    pos = i;
                }
            }
            return pos;
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(long[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void close() {
            writer.close();
        }

    }

    static class IOUtils {
        public static long[] readLongArray(InputReader in, int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; i++) {
                array[i] = in.readLong();
            }
            return array;
        }

    }
}

