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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class D {
	static long INF=(long)1e18;

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt(), k = sc.nextInt(), x = sc.nextInt();

		PriorityQueue<Pair> pqpos = new PriorityQueue<Pair>();
		PriorityQueue<Pair> pqneg = new PriorityQueue<Pair>();
		long[] nums = new long[n];
		for (int i = 0; i < n; i++) {
			nums[i] = sc.nextLong();
			if (nums[i] >= 0) {
				pqpos.add(new Pair(nums[i], i));
			} else
				pqneg.add(new Pair(-nums[i], i));
		}

		// System.out.println(Arrays.toString(nums));

		while (k > 0) {
			boolean neg = (pqneg.size() & 1) == 1;
			
			boolean canbeneg=false;
			
			if (neg) {
				Pair posmin = pqpos.peek();
				Pair negmin = pqneg.peek();
				if(pqpos.isEmpty())
					posmin=new Pair(INF,-1);
				if(pqneg.isEmpty())
					negmin=new Pair(INF,-1);

				if (posmin.x <= negmin.x) {
					pqpos.poll();
					pqpos.add(new Pair(posmin.x + x, posmin.y));
				} else {
					pqneg.poll();
					pqneg.add(new Pair(negmin.x + x, negmin.y));
				}
			} else {
				
				Pair posmin = pqpos.peek();
				Pair negmin = pqneg.peek();
				if(pqpos.isEmpty())
					posmin=new Pair(INF,-1);
				if(pqneg.isEmpty())
					negmin=new Pair(INF,-1);
				if(posmin.x<=negmin.x){
					pqpos.poll();
					if(posmin.x-x>=0)
						pqpos.add(new Pair(posmin.x-x,posmin.y));
					else
						pqneg.add(new Pair(x-posmin.x,posmin.y));
				}
				else{
					pqneg.poll();
					if(negmin.x-x>0)
						pqneg.add(new Pair(negmin.x-x,negmin.y));
					else
						pqpos.add(new Pair(x-negmin.x,negmin.y));
					
				}
					
			}
			k--;
		}
		while(!pqneg.isEmpty()){
			Pair p=pqneg.poll();
			
			nums[p.y]=-p.x;
		}
		while(!pqpos.isEmpty()){
			Pair p= pqpos.poll();
			nums[p.y]=p.x;
		}
		for (int i = 0; i < nums.length; i++) {
			out.print(nums[i]+" ");
		}
		out.flush();
		out.close();
	}

	
	static class Pair implements Comparable<Pair> {
		long x;
		int y;

		public Pair(long a, int b) {
			x = a;
			y = b;
		}

		public int compareTo(Pair o) {
			if ((x - o.x) > 0)
				return 1;
			if ((x - o.x) < 0)
				return -1;

			return (y - o.y);
		}

		public String toString() {
			return x + " " + y;
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}
}
