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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class DTask {

    static long[] arr;
    static long k;
    static long x;

    public static void main(String[] args) throws IOException {
        MyInputReader in = new MyInputReader(System.in);
        int n = in.nextInt();
        k = in.nextInt();
        x = in.nextInt();
        arr = new long[n];
        boolean pos = true;
        for (int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
            if (arr[i] < 0) {
                pos = !pos;
            }
        }
        pos = removeZeros(pos);
        int pl = 1;
        for (int i = 0; i < n; i++) {
            pl *= Math.signum(arr[i]);
        }
        if (pl == 1) {
            makeNeg();
        }
        check();
        Comparator<Integer> cmp = (o1, o2) -> Long.compare(Math.abs(arr[o1]), Math.abs(arr[o2]));
        PriorityQueue<Integer> pq = new PriorityQueue<>(cmp);
        for (int i = 0; i < arr.length; i++) {
            pq.add(i);
        }
        while (k > 0) {
            int i = pq.poll();
            if (arr[i] > 0) {
                arr[i] += x;
            } else {
                arr[i] -= x;
            }
            k--;
            pq.add(i);
        }
        check();
    }

    static void makeNeg() {
        check();
        int idx = 0;
        for (int i = 0; i < arr.length; i++) {
            if (Math.abs(arr[i]) < Math.abs(arr[idx])) {
                idx = i;
            }
        }
        if (arr[idx] > 0) {
            while (arr[idx] >= 0) {
                check();
                arr[idx] -= x;
                k--;
            }
        } else {
            while (arr[idx] <= 0) {
                check();
                arr[idx] += x;
                k--;
            }
        }
    }

    static boolean removeZeros(boolean pos) {
        for (int i = 0; i < arr.length; i++) {
            check();
            if (arr[i] == 0) {
                if (pos) {
                    arr[i] = -x;
                    pos = false;
                } else {
                    arr[i] = x;
                }
                k--;
            }
        }
        return pos;
    }

    static void check() {
        if (k == 0) {
            for (int i = 0; i < arr.length; i++) {
                System.out.print(arr[i] + " ");
            }
            System.exit(0);
        }
    }

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

        public MyInputReader(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());
        }
    }

}