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;
struct num {
  long long value;
  bool sign;
  int idx;
  num(long long v, bool s, int i) : value(v), sign(s), idx(i) {}
};
bool operator<(num const& a, num const& b) { return a.idx < b.idx; }
struct compare {
  bool operator()(num const& a, num const& b) { return a.value > b.value; }
};
int main() {
  priority_queue<num, vector<num>, compare> q;
  long long n, k, x;
  cin >> n >> k >> x;
  int neg = 0;
  long long a[n];
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] < 0) neg++;
  }
  for (int i = 0; i < n; i++) q.push(num(abs(a[i]), (a[i] < 0 ? 1 : 0), i));
  while (k--) {
    num cur = q.top();
    q.pop();
    if (neg % 2 == 0) {
      cur.value -= x;
      if (cur.value < 0) {
        cur.sign = !cur.sign;
        cur.value = abs(cur.value);
        neg++;
      }
    } else
      cur.value += x;
    q.push(cur);
  }
  set<num> res;
  while (!q.empty()) {
    num cur = q.top();
    q.pop();
    res.insert(cur);
  }
  for (num e : res) {
    if (e.sign)
      cout << e.value * -1 << " ";
    else
      cout << e.value << " ";
  }
  cout << endl;
}
