#include<bits/stdc++.h>
using namespace std;
long long int N,M,K,T,H,W,L,R;
int main()
{
	cin>>N>>M>>K;
	N=abs(N);
	long long int num=N/K;
	if(num>=M)
	{
		cout<<N-M*K;
		return 0;
	}
	H=N%K;
	if((M-num)&1)
	{
		cout<<K-H;
	}
	else
	{
		cout<<H;
		
	}
}
### 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<bits/stdc++.h>
using namespace std;
long long int N,M,K,T,H,W,L,R;
int main()
{
	cin>>N>>M>>K;
	N=abs(N);
	long long int num=N/K;
	if(num>=M)
	{
		cout<<N-M*K;
		return 0;
	}
	H=N%K;
	if((M-num)&1)
	{
		cout<<K-H;
	}
	else
	{
		cout<<H;
		
	}
}
```