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

int main(){
    ll X,K,D; cin>>X>>K>>D;
    ll now=abs(X);
    ll num=min(K,now/D);
    K-=num;
    now-=num*D;

    if(K%2==0){
        cout<<now<<endl;
    }else{
        cout<<D-now<<endl;
    }
}
### Prompt

Construct a CPP code solution to the problem outlined:

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;
using ll =long long;

int main(){
    ll X,K,D; cin>>X>>K>>D;
    ll now=abs(X);
    ll num=min(K,now/D);
    K-=num;
    now-=num*D;

    if(K%2==0){
        cout<<now<<endl;
    }else{
        cout<<D-now<<endl;
    }
}
```