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
#include<iostream>
using namespace std;
long X,K,D;
int main()
{
	cin>>X>>K>>D;
	if(X<0)X=-X;
	if(X/D>=K)
	{
		X-=K*D;
		cout<<X<<endl;
		return 0;
	}
	long t=X/D;
	K-=t;
	X-=t*D;
	if(K%2==0)cout<<X<<endl;
	else cout<<D-X<<endl;
}
