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.*;

public class D {
    public static void solution(BufferedReader reader, PrintWriter out)
            throws IOException {
        In in = new In(reader);
        int n = in.nextInt(), k = in.nextInt(), x = in.nextInt();
        PriorityQueue<Num> nums = new PriorityQueue<Num>();
        boolean even = true;
        for (int i = 0; i < n; i++) {
            int a = in.nextInt();
            if (a < 0)
                even = !even;
            nums.add(new Num(a, i));
        }
        for (int i = 0; i < k; i++) {
            Num num = nums.poll();
            long a = num.a;
            if ((a >= 0 && even) || (a < 0 && !even))
                a -= x;
            else
                a += x;
            if ((num.a < 0 && a >= 0) || (num.a >= 0 && a < 0))
                even = !even;
            nums.add(new Num(a, num.id));
        }
        long[] array = new long[n];
        for (Num num : nums)
            array[num.id] = num.a;
        for (Long a : array)
            out.printf("%d ", a);
    }

    protected static class Num implements Comparable<Num> {
        protected long a;
        protected int id;

        public Num(long a, int id) {
            super();
            this.a = a;
            this.id = id;
        }

        @Override
        public int compareTo(Num num) {
            return Long.compare(Math.abs(a), Math.abs(num.a));
        }

    }

    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(
                new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(
                new BufferedWriter(new OutputStreamWriter(System.out)));
        solution(reader, out);
        out.close();
    }

    protected static class In {
        private BufferedReader reader;
        private StringTokenizer tokenizer = new StringTokenizer("");

        public In(BufferedReader reader) {
            this.reader = reader;
        }

        public String next() throws IOException {
            while (!tokenizer.hasMoreTokens())
                tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }

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

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

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