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.util.Comparator;
import java.util.Scanner;
import java.util.TreeSet;

public class Main {
    private static class MyClass {
        public long data;
        public int index;
        public MyClass(long data, int index) {
            this.data = data;
            this.index = index;
        }
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        int k=sc.nextInt();
        int x=sc.nextInt();
        long[] a=new long[n+5];
        for(int i=0;i<n;i++)
            a[i]=sc.nextLong();
        TreeSet<MyClass> ts = new TreeSet<>(new Comparator<MyClass>() {
            @Override
            public int compare(MyClass o1, MyClass o2) {
                long l=Math.abs(o1.data)-Math.abs(o2.data);
                if(l>0)
                    return 1;
                else if(l<0)
                    return -1;
                else
                    return o1.index-o2.index;
            }
        });
        int minus=0;
        for (int i = 0; i < n; i++) {
            ts.add(new MyClass(a[i], i));
            if(a[i]<0)
                minus++;
        }
        while(k>0) {
            if((minus&1) == 0) { //偶数个负数
                MyClass c1 = ts.ceiling(new MyClass(0, 1));
                if(c1.data==0) {
                    int id=c1.index;
                    a[id]-=x;
                    minus++;
                    ts.remove(c1);
                    ts.add(new MyClass(a[id], id));
                }
                else { //没有0
                    c1 = ts.first();
                    int id = c1.index;
                    if(a[id]<0) {
                        a[id]+=x;
                        if(a[id]>=0)
                            minus--;
                    }
                    else {
                        a[id]-=x;
                        if(a[id]<0)
                            minus++;
                    }
                    ts.remove(c1);
                    ts.add(new MyClass(a[id], id));
                }
            }
            else {
                MyClass c1 = ts.ceiling(new MyClass(0, 1));
                if(c1.data==0) {
                    int id=c1.index;
                    a[id]+=x;
                    ts.remove(c1);
                    ts.add(new MyClass(a[id], id));
                }
                else {
                    c1 = ts.first();
                    int id = c1.index;
                    if(a[id]<0) 
                        a[id]-=x;
                    else
                        a[id]+=x;
                    ts.remove(c1);
                    ts.add(new MyClass(a[id], id));
                }
            }
            k--;
        }
        for(int i=0;i<n-1;i++) {
            System.out.print(a[i]+" ");
        }
        System.out.println(a[n-1]);
    }
}