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 <bits/stdc++.h>
using namespace std;
int main()
{
	long long a,b,c;
	cin>>a>>b>>c;
	if (a<0)
		a=abs(a);
	if (b>=a/c)
	{
		if ((b-a/c)%2==0)
		{
			cout<<a%c<<endl;
		}
		else
		{
			cout<<c-(a%c)<<endl;
		}
	}
	else
	{
		cout<<a-b*c<<endl;
	}
	return 0;
}
