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.InputStreamReader;
import java.io.PrintWriter;
import java.util.PriorityQueue;

public class d {
	public static void main(String[] args) throws IOException{
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String[] line = in.readLine().split(" ");
		int n = Integer.parseInt(line[0]);
		int k = Integer.parseInt(line[1]);
		long x = Long.parseLong(line[2]);
		PriorityQueue<Num> pq = new PriorityQueue<Num>();
		boolean positive = true;
		line = in.readLine().split(" ");
		for(int i = 0; i<n; i++){
			pq.add(new Num(Long.parseLong(line[i]),i));
			if(!(Long.parseLong(line[i])>=0L)){
				positive = !positive;
			}
		}
		int used = 0;
		while(used<k && positive){
			used++;
			Num now = pq.poll();
			if(now.abs-x<0){
				positive = false;
				now.pos = !now.pos;
			}
			now.abs = Math.abs(now.abs-x);
			pq.add(now);
		}
		while(used<k){
			used++;
			Num now = pq.poll();
			now.abs +=x;
			pq.add(now);
		}
		long[] ar = new long[n];
		while(pq.size()>0){
			Num now = pq.poll();
			ar[now.id] = now.abs;
			if(!now.pos){
				ar[now.id]*=-1L;
			}
		}
		PrintWriter out = new PrintWriter(System.out);
		for(int i = 0; i<n; i++){
			out.print(ar[i]+" ");
		}
		out.println();
		out.flush();
		out.close();
		
	}
	public static class Num implements Comparable<Num>{
		public long abs;
		public boolean pos;
		public int id;
		public Num(long a, int b){
			abs = a;
			pos = abs>=0L;
			abs = Math.abs(abs);
			
			id = b;
		}
		public int compareTo(Num o){
			return Long.compare(abs, o.abs);
		}
	}
}
