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

int main(){
  ll x,k,d;
  cin>>x>>k>>d;
  if(x<0){
    x*=-1;
  }
  if(x/d>k){
    cout<<x-d*k<<endl;
    return 0;
  }
  k-=x/d;
  x%=d;
  k%=2;
  cout<<abs(x-k*d)<<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>
#define ll long long
using namespace std;

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