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;
#define ll long long
 
int main()
{
	ll x,k,d;
	cin>>x>>k>>d;
	if(abs(x)/d<=k)
	{	
		if((k-abs(x)/d)%2==0){
			cout<<abs(x)%d<<"\n";
		}
		else
			cout<<abs(abs(x)%d-d)<<"\n";
	}
	else
		cout<<abs(x)-k*d<<"\n";
}