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 
//package olymp_prog;

import javafx.collections.transformation.SortedList;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.PriorityQueue;

/**
 * Created by Максим on 13.01.2017.
 */
public class D721 {
    private static class A implements Comparable {
        int n;
        BigInteger val;

        A(BigInteger val, int n) {
            this.val = val;
            this.n = n;
        }

        @Override
        public int compareTo(Object o) {
            return val.abs().compareTo(((A)o).val.abs());
        }
    }
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(
                new InputStreamReader(System.in)
        );
        String raw[] = in.readLine().split(" ");
        int n;
        BigInteger k, x;
        n = Integer.parseInt(raw[0]);
        k = new BigInteger(raw[1]);
        x = new BigInteger(raw[2]);
        raw = in.readLine().split(" ");
        PriorityQueue<A> a = new PriorityQueue<>(n);
        int sgn = 1;
        BigInteger cur = null;
        for (int i = 0; i < n; i++) {
            cur = new BigInteger(raw[i]);
            a.add(new A(cur, i));
            sgn *= cur.compareTo(BigInteger.ZERO) < 0 ? -1 : 1;
        }
//        System.out.println("sgn = " + sgn);
//        System.out.println("Math.abs(a[0].val) - k * x = " + (Math.abs(a[0].val) - k * x));

        if (sgn == 1 && a.peek().val.abs().subtract(k.multiply(x)).compareTo(BigInteger.ZERO) >= 0) {
            a.peek().val = a.peek().val.add(a.peek().val.compareTo(BigInteger.ZERO) < 0 ? k.multiply(x): BigInteger.ZERO.subtract(k).multiply(x));
        } else {
            BigInteger times = BigInteger.valueOf(Math.abs(a.peek().val.intValue()) / x.intValue() + 1);

//            System.out.println("a[0].val = " + a[0].val);
            if (sgn == 1) {
                A tmp = a.poll();
                tmp.val = tmp.val.add(tmp.val.compareTo(BigInteger.ZERO) < 0 ? x.multiply(times) : BigInteger.ZERO.subtract(x).multiply(times));
                k = k.subtract(times);
                a.add(tmp);
            }
//            System.out.println("a[0] = " + a[0].val);
            int kk = k.intValue();
            for (int i = 0; i < kk; i++) {
                A tmp = a.poll();
                tmp.val = tmp.val.add(tmp.val.compareTo(BigInteger.ZERO) >= 0 ? x : BigInteger.ZERO.subtract(x));
                a.add(tmp);
            }
        }
        BigInteger res[] = new BigInteger[n];
        for (A r : a) {
            res[r.n] = r.val;
        }
        for(BigInteger r : res) {
            System.out.print(r + " ");
        }
    }
}
