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.InputStreamReader;
import java.util.PriorityQueue;

public class ProblemD {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] tmp = br.readLine().split(" ");
		int n = Integer.parseInt(tmp[0]);
		int k = Integer.parseInt(tmp[1]);
		int x = Integer.parseInt(tmp[2]);

		Num[] num = new Num[n];
		PriorityQueue<Num> pq = new PriorityQueue<Num>(n);
		tmp = br.readLine().split(" ");
		boolean isPositive = true;
		for (int i = 0; i < n; i++) {
			num[i] = new Num(Integer.parseInt(tmp[i]));
			pq.add(num[i]);

			if (num[i].val < 0) {
				isPositive = !isPositive;
			}
		}

		for (int i = 0; i < k; i++) {
			Num minAbs = pq.poll();
			if (isPositive) {
				if (minAbs.val == 0) {
					minAbs.val -= x;
					isPositive = false;
				} else if (minAbs.val > 0) {
					minAbs.val -= x;
					if (minAbs.val < 0) {
						isPositive = false;
					}
				} else {
					minAbs.val += x;
					if (minAbs.val >= 0) {
						isPositive = false;
					}
				}
			} else {
				if (minAbs.val == 0) {
					minAbs.val += x;
				} else if (minAbs.val > 0) {
					minAbs.val += x;
				} else {
					minAbs.val -= x;
				}
			}
			pq.add(minAbs);
		}
		
		for (int i=0; i<n; i++) {
			System.out.print(num[i].val + " ");
		}
	}

	static class Num implements Comparable<Num> {
		long val;

		Num(int val) {
			this.val = val;
		}

		@Override
		public int compareTo(Num num) {
			return Long.compare(Math.abs(this.val), Math.abs(num.val));
		}
	}
}
