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>
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
void ip(int flag, int x) {
  if (flag == 1)
    printf("%d ", x);
  else
    printf("%d\n", x);
}
void lp(int flag, long long x) {
  if (flag == 1)
    printf("%lld ", x);
  else
    printf("%lld\n", x);
}
using namespace std;
const int maxn = 2e5 + 10;
struct node {
  long long val;
  int num;
  node(long long _val, int _num) {
    val = _val;
    num = _num;
  }
};
bool operator<(const node a, const node b) { return a.val > b.val; }
priority_queue<node> que;
struct QQQ {
  long long val, num;
} cs[maxn];
bool cmp1(QQQ a, QQQ b) { return a.val < b.val; }
bool cmp2(QQQ a, QQQ b) { return a.num < b.num; }
int main() {
  int n, k;
  long long x;
  scanf("%d %d %lld", &n, &k, &x);
  for (int i = int(1); i <= int(n); ++i) {
    scanf("%lld", &cs[i].val);
    cs[i].num = i;
  }
  sort(cs + 1, cs + n + 1, cmp1);
  int st = 0;
  while (st + 1 <= n && cs[st + 1].val < 0) st++;
  if (st == 0) {
    if (cs[1].val >= x * k)
      cs[1].val -= x * k;
    else {
      int ti = ceil(cs[1].val / x);
      k -= ti;
      cs[1].val -= x * ti;
      que.push(node(-cs[1].val, 1));
      for (int i = int(2); i <= int(n); ++i) que.push(node(cs[i].val, i));
      while (k--) {
        node now = que.top();
        que.pop();
        if (now.num == 1)
          cs[1].val -= x;
        else
          cs[now.num].val += x;
        que.push(node(now.val + x, now.num));
      }
    }
  } else if (st == n) {
    if (st % 2 == 1) {
      for (int i = int(1); i <= int(n); ++i) que.push(node(-cs[i].val, i));
      while (k--) {
        node now = que.top();
        que.pop();
        cs[now.num].val -= x;
        que.push(node(now.val + x, now.num));
      }
    } else {
      if (-cs[n].val >= x * k)
        cs[n].val += x * k;
      else {
        int ti = ceil(-cs[n].val / x);
        k -= ti;
        cs[n].val += x * ti;
        for (int i = int(1); i <= int(n - 1); ++i)
          que.push(node(-cs[i].val, i));
        que.push(node(cs[n].val, n));
        while (k--) {
          node now = que.top();
          que.pop();
          if (now.num == n)
            cs[now.num].val += x;
          else
            cs[now.num].val -= x;
          que.push(node(now.val + x, now.num));
        }
      }
    }
  } else {
    if (st % 2 == 1) {
      for (int i = int(1); i <= int(st); ++i) que.push(node(-cs[i].val, i));
      for (int i = int(st + 1); i <= int(n); ++i) que.push(node(cs[i].val, i));
      while (k--) {
        node now = que.top();
        que.pop();
        if (now.num <= st)
          cs[now.num].val -= x;
        else
          cs[now.num].val += x;
        que.push(node(now.val + x, now.num));
      }
    } else {
      if (-cs[st].val >= x * k && cs[st + 1].val >= x * k) {
        if (-cs[st].val <= cs[st + 1].val)
          cs[st].val += x * k;
        else
          cs[st + 1].val -= x * k;
      } else {
        if (-cs[st].val < cs[st + 1].val) {
          int ti = ceil(-cs[st].val / x);
          k -= ti;
          cs[st].val += x * ti;
          for (int i = int(1); i <= int(st - 1); ++i)
            que.push(node(-cs[i].val, i));
          for (int i = int(st); i <= int(n); ++i) que.push(node(cs[i].val, i));
          while (k--) {
            node now = que.top();
            que.pop();
            if (now.num < st)
              cs[now.num].val -= x;
            else
              cs[now.num].val += x;
            que.push(node(now.val + x, now.num));
          }
        } else {
          int ti = ceil(cs[st + 1].val / x);
          k -= ti;
          cs[st + 1].val -= x * ti;
          for (int i = int(1); i <= int(st + 1); ++i)
            que.push(node(-cs[i].val, i));
          for (int i = int(st + 2); i <= int(n); ++i)
            que.push(node(cs[i].val, i));
          while (k--) {
            node now = que.top();
            que.pop();
            if (now.num <= st + 1)
              cs[now.num].val -= x;
            else
              cs[now.num].val += x;
            que.push(node(now.val + x, now.num));
          }
        }
      }
    }
  }
  sort(cs + 1, cs + n + 1, cmp2);
  for (int i = int(1); i <= int(n); ++i) lp(1, cs[i].val);
  return 0;
}
