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 maxn = 200000 + 5;
struct Node {
  long long val;
  int id;
  Node(long long val, int id) : val(val), id(id) {}
  Node() {}
  bool operator<(const Node& rhs) const { return abs(val) > abs(rhs.val); }
};
long long a[maxn];
int n, k;
long long x;
bool cmp(const Node& a, const Node& b) { return a.id < b.id; }
int main() {
  while (cin >> n >> k >> x) {
    int cnt = 0;
    priority_queue<Node> pq;
    memset(a, 0, sizeof(a));
    for (int i = 0; i < n; i++) {
      cin >> a[i];
      pq.push(Node(a[i], i));
      if (a[i] < 0) cnt++;
    }
    for (int i = 0; i < k; i++) {
      Node u = pq.top();
      pq.pop();
      if (cnt % 2 == 1) {
        if (u.val >= 0) {
          u.val += x;
        } else {
          u.val -= x;
        }
        pq.push(u);
      } else {
        if (u.val >= 0) {
          u.val -= x;
          if (u.val < 0) cnt++;
        } else {
          u.val += x;
          if (u.val >= 0) cnt--;
        }
        pq.push(u);
      }
    }
    vector<Node> ans;
    while (!pq.empty()) {
      ans.push_back(pq.top());
      pq.pop();
    }
    sort(ans.begin(), ans.end(), cmp);
    cout << ans[0].val;
    for (int i = 1; i < n; i++) cout << " " << ans[i].val;
    cout << endl;
  }
  return 0;
}
