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.*;

public class D {
	InputStream is;

	int __t__ = 1;
	int __f__ = 0;
	int __FILE_DEBUG_FLAG__ = __f__;
	String __DEBUG_FILE_NAME__ = "src/D4";

	FastScanner in;
	PrintWriter out;

	class State implements Comparable<State> {
		int id;
		long val;

		State(int id, long val) {
			this.id = id;
			this.val = val;
		}

		public int compareTo(State s) {
			return Long.compare(val, s.val);
		}

		public String toString() {
			return "(" + id + ", " + val + ")";
		}
	}
	public void solve() {
		int n = in.nextInt(), k = in.nextInt(), x = in.nextInt();
		int[] a = in.nextIntArray(n);
		
		int neg = 0, pos = 0, zero = 0;
		int negMax = Integer.MIN_VALUE, posMin = Integer.MAX_VALUE;
		int negMaxIdx = -1, posMinIdx = -1;
		List<Integer> zeroIdxs = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			if (a[i] > 0) {
				pos++;
				if (a[i] < posMin) {
					posMin = a[i];
					posMinIdx = i;
				}
			} else if (a[i] < 0) {
				neg++;
				if (a[i] > negMax) {
					negMax = a[i];
					negMaxIdx = i;
				}
			} else {
				zero++;
				zeroIdxs.add(i);
			}
		}

		long[] b = new long[n];
		for (int i = 0; i < n; i++) b[i] = a[i];
		
		if (k < zeroIdxs.size()) {
			for (int i = 0; i < n; i++) out.print(b[i] + " ");
			out.println();
			out.close();
			return;
		}
		
		int restK = k;
		for (int zeroIdx : zeroIdxs) {
			restK--;
			assert b[zeroIdx] == 0;
			if (neg % 2 == 0) {
				b[zeroIdx] -= x;
				neg++;
			} else {
				b[zeroIdx] += x;
				pos++;
			}
		}
		
		if (neg % 2 == 0) {
			if (neg == 0 || (pos != 0 && Math.abs(posMin) < Math.abs(negMax))) {
				while (restK > 0 && b[posMinIdx] >= 0) {
					b[posMinIdx] -= x;
					restK--;
				}
			} else {
				while (restK > 0 && b[negMaxIdx] <= 0) {
					b[negMaxIdx] += x;
					restK--;
				}
			}
		}
		
		PriorityQueue<State> pq = new PriorityQueue<>();
		for (int i = 0; i < n; i++) {
			pq.add(new State(i, Math.abs(b[i])));
		}
		
		while (restK > 0) {
			State ns = pq.poll();
			b[ns.id] += (b[ns.id] > 0) ? x : -x;
			pq.add(new State(ns.id, (b[ns.id] > 0) ? b[ns.id] : -b[ns.id]));
			restK--;
		}
		
		for (int i = 0; i < n; i++) out.print(b[i] + " ");
		out.println();
		out.close();
	}

	public void run() {
		if (__FILE_DEBUG_FLAG__ == __t__) {
			try {
				is = new FileInputStream(__DEBUG_FILE_NAME__);
			} catch (FileNotFoundException e) {
				// TODO 自動生成された catch ブロック
				e.printStackTrace();
			}
			System.out.println("FILE_INPUT!");
		} else {
			is = System.in;
		}
		in = new FastScanner(is);
		out = new PrintWriter(System.out);

		solve();
	}

	public static void main(String[] args) {
		new D().run();
	}

	public void mapDebug(int[][] a) {
		System.out.println("--------map display---------");

		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}

		System.out.println("----------------------------");
		System.out.println();
	}

	public void debug(Object... obj) {
		System.out.println(Arrays.deepToString(obj));
	}

	class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
			//stream = new FileInputStream(new File("dec.in"));

		}

		int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

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

		int[] nextIntArray(int n) {
			return nextIntArray(n, 0);
		}

		int[] nextIntArray(int n, int margin) {
			int[] array = new int[n + margin];
			for (int i = 0; i < n; i++)
				array[i + margin] = nextInt();

			return array;
		}

		int[][] nextIntMap(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextIntArray(m);
			}
			return map;
		}

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

		long[] nextLongArray(int n) {
			return nextLongArray(n, 0);
		}

		long[] nextLongArray(int n, int margin) {
			long[] array = new long[n + margin];
			for (int i = 0; i < n; i++)
				array[i + margin] = nextLong();

			return array;
		}

		long[][] nextLongMap(int n, int m) {
			long[][] map = new long[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextLongArray(m);
			}
			return map;
		}

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

		double[] nextDoubleArray(int n) {
			return nextDoubleArray(n, 0);
		}

		double[] nextDoubleArray(int n, int margin) {
			double[] array = new double[n + margin];
			for (int i = 0; i < n; i++)
				array[i + margin] = nextDouble();

			return array;
		}

		double[][] nextDoubleMap(int n, int m) {
			double[][] map = new double[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextDoubleArray(m);
			}
			return map;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}

