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.*;
import java.math.*;
import static java.lang.Math.*;
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.Double.parseDouble;
import static java.lang.String.*;

public class Main {
    
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder out = new StringBuilder();
        StringTokenizer tk;
        
        tk = new StringTokenizer(in.readLine());
        int n = parseInt(tk.nextToken()),k = parseInt(tk.nextToken()),x = parseInt(tk.nextToken());
        
        Queue<Integer> z = new LinkedList<>();
        Queue<pair> num = new PriorityQueue<>();
        long [] ans = new long[n];
        int neg=0,pos=0;
        
        tk = new StringTokenizer(in.readLine());
        for(int i=0; i<n; i++) {
            int v = parseInt(tk.nextToken());
            if(v==0) z.add(i);
            else {
                num.add(new pair(i,v));
                if(v<0) neg++;
                else pos++;
            }
        }
        
        if(z.size()>k) {
            while(!num.isEmpty())
                ans[num.peek().i] = num.remove().v;
            
            for(int i=0; i<n; i++)
                out.append(ans[i]).append(" ");
            System.out.println(out);
            
            return;
        }
        
        while(!z.isEmpty()) {
            int i = z.remove();
            
            if(z.isEmpty() && neg%2==0) {
                num.add(new pair(i,-x));
                neg++;
                k--;
            } else {
                num.add(new pair(i,x));
                pos++;
                k--;
            }
        }
        
        while(!num.isEmpty() && k > 0) {
            pair cur = num.remove();
            
            if(neg%2==0) {
                if(cur.v<0) {
                    long c = (long)ceil((double)abs(cur.v)/x);
                    if(abs(cur.v)%x==0) c++;
                    while(c>0) {
                        if(c <= k) {
                            k -= c;
                            cur.v += c*x;
                            neg--;
                            break;
                        }
                        c--;
                    }
                    if(c==0) {
                        num.add(cur);
                        break;
                    }
                } else {
                    long c = (long)ceil((double)cur.v/x);
                    if(cur.v%x==0) c++;
                    while(c>0) {
                        if(c <= k) {
                            k -= c;
                            cur.v -= c*x;
                            neg++;
                            break;
                        }
                        c--;
                    }
                    if(c==0) {
                        num.add(cur);
                        break;
                    }
                }
            } else {
                num.add(cur);
                break;
            }
            num.add(cur);
        }
        
        while(!num.isEmpty() && k>0) {
            pair cur = num.remove();
            if(cur.v < 0) {
                cur.v -= x;
                k--;
            } else {
                cur.v += x;
                k--;
            }
            
            num.add(cur);
        }
        
        while(!num.isEmpty())
            ans[num.peek().i] = num.remove().v;
        
        for(int i=0; i<n; i++)
            out.append(ans[i]).append(" ");
        
        System.out.println(out);
    }
    
}

class pair implements Comparable<pair> {
    int i;
    long v;
    
    public pair(int i,long v) {
        this.i = i;
        this.v = v;
    }
    
    @Override
    public int compareTo(pair p) {
        if(abs(v) != abs(p.v))
            return Long.compare(abs(v),abs(p.v));
        return i-p.i;
    }
    
    @Override
    public String toString() {
        return "("+i+","+v+")";
    }
}