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.util.PriorityQueue;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author MottoX
 */
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);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }

    static class Task {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt(), k = in.nextInt(), x = in.nextInt();
            long[] a = new long[n];

            PriorityQueue<Pair<Long, Integer>> queue =
                    new PriorityQueue<>((o1, o2) -> Long.compare(Math.abs(o1.first), Math.abs(o2.first)));

            int sign = 1;
            for (int i = 0; i < n; i++) {
                a[i] = in.nextLong();
                queue.add(Pair.of(a[i], i));
                if (a[i] < 0) {
                    sign = -sign;
                }
            }

            while (k-- > 0) {
                Pair<Long, Integer> peek = queue.poll();
                long number = peek.first;
                int pos = peek.second;
                if (number < 0) {
                    sign = -sign;
                }
                if (sign >= 0) {
                    a[pos] -= x;
                    if (a[pos] < 0) {
                        sign = -sign;
                    }
                } else {
                    a[pos] += x;
                }
                queue.add(Pair.of(a[pos], pos));
            }

            for (long val : a) {
                out.print(val + " ");
            }
        }

    }

    static class Pair<K, V> implements Comparable<Pair<K, V>> {
        public final K first;
        public final V second;

        public Pair(K first, V second) {
            this.first = first;
            this.second = second;
        }

        public static <K, V> Pair<K, V> of(K first, V second) {
            return new Pair<>(first, second);
        }

        public boolean equals(final Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }
            Pair pair = (Pair) o;
            return !(first != null ? !first.equals(pair.first) : pair.first != null) &&
                    !(second != null ? !second.equals(pair.second) : pair.second != null);
        }

        public int hashCode() {
            int result = first != null ? first.hashCode() : 0;
            result = 31 * result + (second != null ? second.hashCode() : 0);
            return result;
        }

        @SuppressWarnings("unchecked")

        public int compareTo(Pair<K, V> o) {
            int v = ((Comparable<K>) first).compareTo(o.first);
            return v != 0 ? v : ((Comparable<V>) second).compareTo(o.second);
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

    }

    static class InputReader {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            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());
        }

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

    }
}

