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

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

### 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;

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

```