#include <bits/stdc++.h>
using namespace std;

long long x, k, d, one = 1;

int main() {
  cin >> x >> k >> d;
  if (x < 0) one *= -1, x *= -1;
  long long now = min(x / d, k);
  x -= d * now;
  k -= now;
  k %= 2;
  if (k & 1) x -= d;
  cout << abs(x) << endl;
  return 0;
}
### Prompt

Develop a solution in CPP to the problem described below:

Takahashi, who lives on the number line, is now at coordinate X. He will make exactly K moves of distance D in the positive or negative direction.

More specifically, in one move, he can go from coordinate x to x + D or x - D.

He wants to make K moves so that the absolute value of the coordinate of the destination will be the smallest possible.

Find the minimum possible absolute value of the coordinate of the destination.

Constraints

* -10^{15} \leq X \leq 10^{15}
* 1 \leq K \leq 10^{15}
* 1 \leq D \leq 10^{15}
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


X K D


Output

Print the minimum possible absolute value of the coordinate of the destination.

Examples

Input

6 2 4


Output

2


Input

7 4 3


Output

1


Input

10 1 2


Output

8


Input

1000000000000000 1000000000000000 1000000000000000


Output

1000000000000000

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

long long x, k, d, one = 1;

int main() {
  cin >> x >> k >> d;
  if (x < 0) one *= -1, x *= -1;
  long long now = min(x / d, k);
  x -= d * now;
  k -= now;
  k %= 2;
  if (k & 1) x -= d;
  cout << abs(x) << endl;
  return 0;
}
```