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 x,k,d;
	cin>>x>>k>>d;
	x=abs(x);
	if(x/k>=d)
		cout<<abs(x-k*d);
	else
	{
		long long res=x%d;
		long long cnt=(x-res)/d;
		if((k-cnt)%2)
			res=abs(res-d);
		cout<<res;
	}

	return 0; 
}