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.PriorityQueue;
import java.util.Queue;
import java.util.StringTokenizer;

public class D {

    void solve() throws IOException {
        FastScanner scanner = new FastScanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        int x = scanner.nextInt();
        long[] a = new long[n];
        int sign = 1;
        Queue<Item> q = new PriorityQueue<>();
        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
            if (a[i] < 0) {
                sign = -sign;
            }
        }
        for (int i = 0; i < n; i++) {
            if (a[i] == 0 && k > 0) {
                if (sign > 0) {
                    a[i] -= x;
                    sign = -sign;
                } else {
                    a[i] += x;
                }
                k--;
            }
            q.add(new Item(i, a[i]));
        }
        if (sign > 0) {
            int i = q.poll().position;
            int s = sign(a[i]);
            while (k > 0 && sign(a[i]) != -s) {
                k--;
                a[i] += -s * x;
            }
            q.add(new Item(i, a[i]));
        }
        for (int i = 0; i < k; i++) {
            int pos = q.poll().position;
            a[pos] += sign(a[pos]) * x;
            q.add(new Item(pos, a[pos]));
        }
        for (int i = 0; i < n; i++) {
            writer.print(a[i] + " ");
        }
        writer.close();
    }

    int sign(long x) {
        if (x > 0) {
            return 1;
        } else if (x == 0) {
            return 0;
        } else {
            return -1;
        }
    }

    class Item implements Comparable<Item> {
        int position;
        long value;

        public Item(int position, long value) {
            this.position = position;
            this.value = value;
        }

        public int compareTo(Item o) {
            return Long.compare(Math.abs(value), Math.abs(o.value));
        }
    }

    public static void main(String... args) throws IOException {
        new D().solve();
    }

    static class FastScanner {

        BufferedReader br;
        StringTokenizer tokenizer;

        FastScanner(String fileName) throws FileNotFoundException {
            this(new FileInputStream(new File(fileName)));
        }

        FastScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        String nextLine() throws IOException {
            tokenizer = null;
            return br.readLine();
        }

        String next() throws IOException {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = br.readLine();
                if (line == null) {
                    return null;
                }
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }

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