#include<bits/stdc++.h>

using namespace std;

typedef long long ll;

int main(){
    ll x,k,d;cin >> x>>k>>d;
    x=abs(x);

    ll piece=min(k,x/d);
    k-=piece;
    x-=piece*d;

    if(k%2==0){
        cout << x<<endl;
    }else{
        cout << d-x<<endl;
    }
}


### 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;

typedef long long ll;

int main(){
    ll x,k,d;cin >> x>>k>>d;
    x=abs(x);

    ll piece=min(k,x/d);
    k-=piece;
    x-=piece*d;

    if(k%2==0){
        cout << x<<endl;
    }else{
        cout << d-x<<endl;
    }
}


```