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 
#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 1, M = 1e3 + 1;
long long n, k, x;
long long prod = 1;
struct struc {
  long long idx;
  long long val;
  long long sign;
  bool operator<(struc a) const { return val < a.val; }
};
long long a[N];
int main() {
  cin >> n >> k >> x;
  multiset<struc> s;
  int neg = 0, zer = 0;
  for (int i = 0; i < n; i++) {
    long long val;
    cin >> val;
    long long absolute = abs(val);
    struc tmp;
    tmp.val = absolute;
    tmp.idx = i;
    tmp.sign = (val < 0 ? -1 : 1);
    s.insert(tmp);
    if (!val)
      zer++;
    else if (tmp.sign == -1)
      neg++;
    a[i] = val;
  }
  while (k--) {
    auto it = s.begin();
    s.erase(s.begin());
    long long val, idx, sign;
    val = it->val;
    idx = it->idx;
    sign = it->sign;
    if (neg % 2) {
      val += x;
    } else {
      if (val < x)
        val = abs(val - x), sign = -sign, neg++;
      else
        val -= x;
    }
    struc tmp = {idx, val, sign};
    a[idx] = val * sign;
    s.insert(tmp);
  }
  for (int i = 0; i < n; i++) cout << a[i] << " ";
  cout << endl;
}
