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

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

Your challenge is to write a Cpp solution 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<bits/stdc++.h>
using namespace std;

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