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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.util.StringTokenizer;


public class D {

	static StringTokenizer st;
	static BufferedReader br;
	static PrintWriter pw;
	static class Sort implements Comparable<Sort> {
		long val;
		int ind;
		public int compareTo(Sort arg0) {
			if (this.val > arg0.val)
				return 1;
			if (this.val < arg0.val)
				return -1;
			return 0;
		}
		public Sort(long val, int ind) {
			this.val = val;
			this.ind = ind;
		}
	}
	
	public static void main(String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int n = nextInt();
		int k = nextInt();
		int x = nextInt();
		long[]a = new long[n+1];
		for (int i = 1; i <= n; i++) {
			a[i] = nextInt();
		}
		PriorityQueue<Sort> q = new PriorityQueue<>();
		int minus = 0;
		for (int i = 1; i <= n; i++) {
			q.add(new Sort(Math.abs(a[i]), i));
			if (a[i] <= 0)
				minus++;
		}
		for (int i = 1; i <= k; i++) {
			int id = q.peek().ind;
			if (a[id] > 0) {
				if (minus % 2==1)
					a[id] += x;
				else
					a[id] -= x;
				if (a[id] <= 0)
					minus++;
			}
			else {
				if (minus % 2==1)
					a[id] -= x;
				else
					a[id] += x;
				if (a[id] > 0)
					minus--;
			}
			q.poll();
			q.add(new Sort(Math.abs(a[id]), id));
		}
		for (int i = 1; i <= n; i++) {
			pw.print(a[i]+" ");
		}
		pw.close();
	}
	private static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	private static long nextLong() throws IOException {
		return Long.parseLong(next());
	}
	private static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
	private static String next() throws IOException {
		while (st==null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}
}