#include<iostream>
using namespace std;
using ll = long long;

int main() {
  ll X,K,D,ans;
  cin>>X>>K>>D;
  X=abs(X);
  if (X/D>=K) ans = X-K*D;
  else if ((K-X/D)%2 == 0) ans = X%D;
  else ans = D-X%D;
  cout<<ans<<endl;
  return 0;
}

### Prompt

Please create a solution in Cpp to the following problem:

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<iostream>
using namespace std;
using ll = long long;

int main() {
  ll X,K,D,ans;
  cin>>X>>K>>D;
  X=abs(X);
  if (X/D>=K) ans = X-K*D;
  else if ((K-X/D)%2 == 0) ans = X%D;
  else ans = D-X%D;
  cout<<ans<<endl;
  return 0;
}

```