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.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;


public class Ejercicio3 {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		
		int n = s.nextInt();
		int k = s.nextInt();
		int x = s.nextInt();
		
		
		PriorityQueue<Node> pq = new PriorityQueue<>(new Comparator(){

			@Override
			public int compare(Object arg0, Object arg1) {
				// TODO Auto-generated method stub
				return (int) (((Node)arg0).value - ((Node)arg1).value);
			}
			
		});
		Node[] array = new Node[n];
		boolean negative = false;
		for (int i = 0; i < n; i++) {
			
			long number = s.nextLong();
			if(number<0) negative=!negative;
			Node node = new Node(Math.abs(number),i, number<0);
			array[i]=node;
			pq.add(node);
			
			
		}
		
		if(!negative){
			while(k>0 && !negative){
				Node node =pq.poll();
				node.value-=x;
				k--;
				if(node.value<0){
					negative=true;
					node.negative=!node.negative;
					node.value=Math.abs(node.value);
				}
				pq.add(node);
			}
		}
		
		while(k>0){
			Node node =pq.poll();
			node.value+=x;
			k--;
			pq.add(node);
		}
		
		for (int i = 0; i < n; i++) {
			long num = array[i].value;
			if(array[i].negative) num*=-1;
			System.out.print(num+" ");
		}
		
		
	}
	
	
	private static class Node{
		
		public long value;
		public int pos;
		public boolean negative;
		
		Node(long value, int pos, boolean negative){
			this.value=value;
			this.pos=pos;
			this.negative = negative;
		}
	}
}
