#include <bits/stdc++.h>

using namespace std;
long long x, k, d;


int main(){
    cin>>x>>k>>d;
    if (abs(x)/d>k) cout<<abs(x)-k*d;
    else {
        long long m=k-abs(x)/d;
        if (m%2==0) cout<<abs(x)%d;
        else cout<<abs(abs(x)%d-d);
    }
}

### Prompt

Create a solution in CPP for 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;
long long x, k, d;


int main(){
    cin>>x>>k>>d;
    if (abs(x)/d>k) cout<<abs(x)-k*d;
    else {
        long long m=k-abs(x)/d;
        if (m%2==0) cout<<abs(x)%d;
        else cout<<abs(abs(x)%d-d);
    }
}

```