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