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.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class MaximAndArray {

	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();
		long x = sc.nextInt();
		long a[] = new long[n];
		int idx = -1;
		int count = 0;
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextLong();
			if (a[i] < 0)
				count++;
			if (idx == -1 || Math.abs(a[i]) < Math.abs(a[idx]))
				idx = i;
		}
		
		if (count%2 == 0) {
			long c = (Math.abs(a[idx])/x) + 1;
			c = Math.min(c, k);
			if (a[idx] >= 0)
				a[idx] = a[idx] - c*x;
			else
				a[idx] = a[idx] + c*x;
			k -= c;
		}
		
		long res[] = new long[n];
		PriorityQueue<Pair> pq = new PriorityQueue<>();
		
		for (int i = 0; i < n; i++) 
			pq.add(new Pair(a[i], i));
		
		while(k-->0) {
			Pair cur = pq.remove();
			pq.add(new Pair(f(cur.num, x), cur.idx));
		}
		
		while(!pq.isEmpty()) {
			Pair cur = pq.remove();
			res[cur.idx] = cur.num;
		}
		
		for (int i = 0; i < n; i++) {
			if (i > 0)
				out.print(" ");
			out.print(res[i]);
		}
		
		out.flush();
		out.close();
	}
	
	static long f(long a, long val) {
		if (a >= 0)
			return a + val;
		else
			return a - val;
	}
	
	static class Pair implements Comparable<Pair> {
		long num;
		int idx;
		
		public Pair(long n, int i) {
			num = n;
			idx = i;
		}

		@Override
		public int compareTo(Pair o) {
			long n1 = Math.abs(num);
			long n2 = Math.abs(o.num);
			if (n1 != n2)
				return n1 > n2 ? 1 : -1;
			return idx > o.idx ? 1 : -1;
		}
	}
	
	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(FileReader f) {
			br = new BufferedReader(f);
		}

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

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

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

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

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

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

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

		public void waitForInput(long time) {
			long ct = System.currentTimeMillis();
			while(System.currentTimeMillis() - ct < time) {};
		}

	}

}
