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.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.TreeSet;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

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

    static class TaskD {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            int K = in.nextInt();
            int X = in.nextInt();

            TreeSet<TaskD.Num> pos = new TreeSet<>();
            TreeSet<TaskD.Num> zer = new TreeSet<>();
            TreeSet<TaskD.Num> neg = new TreeSet<>();

            for (int i = 0; i < N; i++) {
                int y = in.nextInt();
                if (y > 0) {
                    pos.add(new TaskD.Num(i, y));
                } else if (y == 0) {
                    zer.add(new TaskD.Num(i, y));
                } else {
                    neg.add(new TaskD.Num(i, y));
                }
            }

            if (zer.size() > 0) {
                if (zer.size() > K) {
                    //nic nie musimy robic, lepiej niz zero nie bedzie
                    print(pos, zer, neg, out);
                    return;
                } else {
                    //zrob nie zerowo, utrzymujac nie parzysta liczbe neg
                    if (neg.size() % 2 == 0) {
                        TaskD.Num z = zer.pollFirst();
                        z.value -= X;
                        neg.add(z);
                        K--;
                    }
                    while (!zer.isEmpty()) {
                        TaskD.Num z = zer.pollFirst();
                        z.value += X;
                        pos.add(z);
                        K--;
                    }
                }
            } else if (neg.size() % 2 == 0) {
                if (neg.size() == 0) {
                    //czy da rade najmniejszy z pos zrobic ujemny
                    //czy da rade najmniejszy z pos zrobic zerowy
                    //musza byc positivy
                    TaskD.Num lpos = pos.pollFirst();
                    long toNeg = (lpos.value / X) + 1;
                    long toZer = lpos.value / X;
                    if (toNeg <= K) {
                        lpos.value -= toNeg * X;
                        neg.add(lpos);
                        K -= toNeg;
                    } else if (toZer <= K && lpos.value % X == 0) {
                        lpos.value = 0;
                        zer.add(lpos);
                        K -= toZer;
                    } else {
                        pos.add(lpos);
                    }
                } else {
                    if (pos.size() > 0 && pos.first().value < Math.abs(neg.last().value)) {
                        TaskD.Num lpos = pos.pollFirst();
                        long toNeg = (lpos.value / X) + 1;
                        long toZer = lpos.value / X;
                        if (toNeg <= K) {
                            lpos.value -= toNeg * X;
                            neg.add(lpos);
                            K -= toNeg;
                        } else if (toZer <= K && lpos.value % X == 0) {
                            lpos.value = 0;
                            zer.add(lpos);
                            K -= toZer;
                        } else {
                            pos.add(lpos);
                        }
                    } else {
                        TaskD.Num bneg = neg.pollLast();
                        long toPos = (-bneg.value / X) + 1;
                        long toZer = -bneg.value / X;
                        if (toPos <= K) {
                            bneg.value += toPos * X;
                            pos.add(bneg);
                            K -= toPos;
                        } else if (toZer <= K && bneg.value % X == 0) {
                            bneg.value = 0;
                            zer.add(bneg);
                            K -= toZer;
                        } else {
                            neg.add(bneg);
                        }
                    }
                }
            }

            if (zer.size() > 0) {
                print(pos, zer, neg, out);
                return;
            }

            if (neg.size() % 2 == 0) {
                while (K > 0) {
                    long p1 = pos.size() == 0 ? Long.MAX_VALUE - 1 : pos.first().value;
                    long n1 = neg.size() == 0 ? Long.MIN_VALUE + 1 : neg.last().value;

                    if (p1 < Math.abs(n1)) {
                        TaskD.Num p = pos.pollFirst();
                        p.value -= X;
                        pos.add(p);
                    } else {
                        TaskD.Num n = neg.pollLast();
                        n.value += X;
                        neg.add(n);
                    }

                    K--;
                }

            } else {
                while (K > 0) {
                    long p1 = pos.size() == 0 ? Long.MAX_VALUE - 1 : pos.first().value;
                    long n1 = neg.size() == 0 ? Long.MIN_VALUE + 1 : neg.last().value;

                    if (p1 < Math.abs(n1)) {
                        TaskD.Num p = pos.pollFirst();
                        p.value += X;
                        pos.add(p);
                    } else {
                        TaskD.Num n = neg.pollLast();
                        n.value -= X;
                        neg.add(n);
                    }

                    K--;
                }
            }

            print(pos, zer, neg, out);
        }

        private void print(final TreeSet<TaskD.Num> pos, final TreeSet<TaskD.Num> zer, final TreeSet<Num> neg, final PrintWriter out) {
            int N = pos.size() + zer.size() + neg.size();
            long values[] = new long[N];

            for (TaskD.Num n : pos) {
                values[n.idx] = n.value;
            }
            for (TaskD.Num n : zer) {
                values[n.idx] = n.value;
            }
            for (TaskD.Num n : neg) {
                values[n.idx] = n.value;
            }
            for (int i = 0; i < N; i++) {
                out.print(values[i] + " ");
            }
            out.println();
        }

        private static class Num implements Comparable<TaskD.Num> {
            private int idx;
            private long value;

            public Num(final int idx, final long value) {
                this.idx = idx;
                this.value = value;
            }

            public int compareTo(final TaskD.Num o) {
                if (this.value < o.value) return -1;
                if (this.value > o.value) return +1;
                return this.idx - o.idx;
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}

