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;
long long int powmod(long long int a, long long int b) {
  long long int res = 1;
  a %= 1000000007;
  assert(b >= 0);
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % 1000000007;
    a = a * a % 1000000007;
  }
  return res;
}
long long int gcd(long long int a, long long int b) {
  return b == 0 ? a : gcd(b, a % b);
}
long long int lcm(long long int a, long long int b) {
  return a * (b / gcd(a, b));
}
long long int m, mx = -1, i, j, n, d, cnt = 0, t, q, tmp, flag = 0, k, pos,
                 bpos = 123456789, x, y;
bool compare(pair<long long int, long long int> a,
             pair<long long int, long long int> b) {
  return (abs(a.first) > abs(b.first));
}
std::priority_queue<pair<long long int, long long int>,
                    std::vector<pair<long long int, long long int> >,
                    decltype(&compare)>
    pq(&compare);
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> k >> x;
  long long int nn = 0;
  for (i = 0; i < n; i++) {
    cin >> tmp;
    pq.push(make_pair(tmp, i));
    if (tmp < 0) nn++;
  }
  while (k--) {
    pair<long long int, long long int> pp = pq.top();
    pq.pop();
    if (pp.first >= 0 && nn % 2 == 1)
      pp.first = pp.first + x;
    else if (pp.first < 0 && nn % 2 == 1)
      pp.first = pp.first - x;
    else if (pp.first >= 0 && nn % 2 == 0) {
      pp.first = pp.first - x;
      if (pp.first < 0) nn++;
    } else if (pp.first < 0 && nn % 2 == 0) {
      pp.first = pp.first + x;
      if (pp.first >= 0) nn--;
    }
    pq.push(pp);
  }
  vector<long long int> v(223456);
  while (!pq.empty()) {
    pair<long long int, long long int> pp = pq.top();
    pq.pop();
    v[pp.second] = pp.first;
  }
  for (i = 0; i < n; i++) cout << v[i] << " ";
  return 0;
}
