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>
long long num[200005];
struct node {
  long long x, id;
  node(long long x, long long id) : x(x), id(id) {}
  bool operator<(const node &b) const { return this->x > b.x; }
};
int check(long long n) {
  if (n > 0)
    return 1;
  else if (n < 0)
    return -1;
  else
    return 0;
}
int main() {
  long long n, k, x;
  long long ans = 1;
  std::vector<int> zero;
  std::cin >> n >> k >> x;
  for (int i = 0; i < n; i++) {
    std::cin >> num[i];
    if (!num[i])
      zero.push_back(i);
    else
      ans *= check(num[i]);
  }
  std::priority_queue<node> q;
  if (!zero.empty()) {
    if (ans > 0 && zero.size() % 2 == 0) {
      for (auto i = zero.begin(); i < zero.end() - 1; i++) {
        num[*i] -= x;
        k--;
        if (k == 0) break;
      }
      if (k) {
        num[*(zero.end() - 1)] += x;
        k--;
      }
    } else if (ans > 0 && zero.size() % 2) {
      for (auto i = zero.begin(); i < zero.end(); i++) {
        num[*i] -= x;
        k--;
        if (k == 0) break;
      }
    } else if (ans < 0 && zero.size() % 2 == 0) {
      for (auto i = zero.begin(); i < zero.end(); i++) {
        num[*i] -= x;
        k--;
        if (k == 0) break;
      }
    } else {
      for (auto i = zero.begin(); i < zero.end() - 1; i++) {
        num[*i] -= x;
        k--;
        if (k == 0) break;
      }
      if (k) {
        num[*(zero.end() - 1)] += x;
        k--;
      }
    }
  }
  if (k) {
    zero.clear();
    ans = 1;
    for (int i = 0; i < n; i++) {
      ans *= check(num[i]);
      q.push(node(std::abs(num[i]), i));
    }
    while (k--) {
      node t = q.top();
      q.pop();
      if (ans > 0) {
        if (num[t.id] < 0) {
          ans /= check(num[t.id]);
          num[t.id] += x;
          if (num[t.id] != 0)
            q.push(node(std::abs(num[t.id]), t.id));
          else {
            if (k) {
              k--;
              num[t.id] += x;
              q.push(node(std::abs(num[t.id]), t.id));
            }
          }
          ans *= check(num[t.id]);
        } else {
          ans /= check(num[t.id]);
          num[t.id] -= x;
          if (num[t.id] != 0)
            q.push(node(std::abs(num[t.id]), t.id));
          else {
            if (k) {
              k--;
              num[t.id] -= x;
              q.push(node(std::abs(num[t.id]), t.id));
            }
          }
          ans *= check(num[t.id]);
        }
      } else {
        if (num[t.id] > 0) {
          ans /= check(num[t.id]);
          num[t.id] += x;
          if (num[t.id] != 0)
            q.push(node(std::abs(num[t.id]), t.id));
          else {
            if (k) {
              k--;
              num[t.id] += x;
              q.push(node(std::abs(num[t.id]), t.id));
            }
          }
          ans *= check(num[t.id]);
        } else {
          ans /= check(num[t.id]);
          num[t.id] -= x;
          if (num[t.id] != 0)
            q.push(node(std::abs(num[t.id]), t.id));
          else {
            if (k) {
              k--;
              num[t.id] -= x;
              q.push(node(std::abs(num[t.id]), t.id));
            }
          }
          ans *= check(num[t.id]);
        }
      }
    }
  }
  for (int i = 0; i < n - 1; i++) std::cout << num[i] << " ";
  std::cout << num[n - 1] << std::endl;
  return 0;
}
