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;
inline long long in() {
  int32_t x;
  scanf("%d", &x);
  return x;
}
inline long long lin() {
  long long x;
  scanf("%lld", &x);
  return x;
}
inline string get() {
  char ch[2000010];
  scanf("%s", ch);
  return ch;
}
inline void read(long long *a, long long n) {
  for (long long i = 0; i < n; i++) a[i] = in();
}
template <class blank>
inline void out(blank x) {
  cout << x << "\n";
  exit(0);
}
const long long maxn = 2e5 + 10;
const long long maxm = 1e6 + 10;
const long long maxlg = 21;
const long long base = 29;
const long long mod = 1e9 + 7;
const long long INF = 1e18 + 10;
const long long SQ = 317;
set<pair<long long, long long> > st;
inline long long relax(long long v) {
  if (v < 0) return -v;
  return v;
}
long long a[maxn];
long long sign = 1;
int32_t main() {
  long long n = in(), k = in(), x = in();
  read(a, n);
  for (long long i = 0; i < n; i++) {
    st.insert({relax(a[i]), i});
    if (a[i] < 0) sign *= -1;
  }
  while (k--) {
    pair<long long, long long> num = *st.begin();
    st.erase(num);
    long long where = num.second;
    if (a[where] < 0) sign *= -1;
    if (sign == 1)
      a[where] -= x;
    else
      a[where] += x;
    if (a[where] < 0) sign *= -1;
    st.insert({relax(a[where]), where});
  }
  for (long long i = 0; i < n; i++) cout << a[i] << " ";
  cout << "\n";
}
