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

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

### Prompt

Please provide a cpp coded solution 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;
using ll = long long;

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

```