#include <iostream>
using namespace std;
typedef long long ll;
int main() {
	ll x,k,d;
	cin>>x>>k>>d;
	x=abs(x);
	ll ans;
	if(k<=(x/d)){
	    ans=x-d*k;
	}
	else{
	    if((k-(x/d))%2){
	        ans=d-x%d;
	    }
	    else{
	        ans=x%d;
	    }
	}
	cout<<ans;
	return 0;
}

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

```