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.Arrays;
import java.io.IOException;
import java.util.stream.Collectors;
import java.io.InputStreamReader;
import java.util.TreeSet;
import java.util.Objects;
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<Num> nums = new TreeSet<>();

            int negatives = 0;

            for (int i = 0; i < N; i++) {
                int val = in.nextInt();
                nums.add(new Num(i, val));
                if (val < 0) negatives++;
            }

            if (negatives % 2 == 0) {
                //probujemy zmienic znak najmniejszego
                Num lowest = nums.pollFirst();
                long needed = (lowest.val / X) + 1;
                if (needed <= K) {
                    lowest.val = Math.abs(lowest.val - needed * X);
                    lowest.negative = !lowest.negative;
                } else {
                    lowest.val -= K * X;
                }
                nums.add(lowest);
                K -= Math.min(needed, K);
            }

            while (K-- > 0) {
                Num min = nums.pollFirst();
                min.val += X;
                nums.add(min);
            }

            long ans[] = new long[N];
            for (Num num : nums) {
                ans[num.idx] = num.negative ? -num.val : num.val;
            }

            out.println(Arrays.stream(ans).mapToObj(Objects::toString).collect(Collectors.joining(" ")));

        }

        private static class Num implements Comparable<Num> {
            private int idx;
            private long val;
            private boolean negative;

            public Num(int idx, long val) {
                this.idx = idx;
                this.val = Math.abs(val);
                this.negative = val < 0;
            }

            public int compareTo(Num that) {
                if (this.val < that.val) return -1;
                if (this.val > that.val) return +1;
                return this.idx - that.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());
        }

    }
}

