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 inf = 2e5 + 10;
bool cmp(const string& a, const string& b) { return a.length() < b.length(); }
long long a[inf];
set<pair<long long, long long> > st;
int main() {
  long long n, k, x;
  int tg = 0;
  cin >> n >> k >> x;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    if (a[i] < 0) tg ^= 1;
    st.insert(make_pair(abs(a[i]), i));
  }
  for (int i = 1; i <= k; i++) {
    long long pos = st.begin()->second;
    st.erase(st.begin());
    if (a[pos] < 0) tg ^= 1;
    if (tg)
      a[pos] += x;
    else
      a[pos] -= x;
    if (a[pos] < 0) tg ^= 1;
    st.insert(make_pair(abs(a[pos]), pos));
  }
  for (int i = 1; i <= n; i++) cout << a[i] << " ";
  cout << endl;
}
