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

import java.util.*;
public class Main {

	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);


		try{
long  x=sc.nextLong();
 long k=sc.nextLong();
long d=sc.nextLong();
long steps=Math.abs(x)/d;
long remaining=k-steps;

long ans=0;
if(x>=0) {

if(k>=steps) {
	ans=x%d;
	if(remaining%2==0) {
		ans=ans;
	}else {
		ans-=d;
	}
	System.out.println(Math.abs(ans));
}else {
	x-=k*d;
	System.out.println(Math.abs(x));

}
}else {
	if(k>=steps) {
		ans=x+steps*d;
		if(remaining%2==0) {
		ans=ans;
		}else {
			ans+=d;
		}
		System.out.println(Math.abs(ans));
	}else {
		x+=k*d;
		System.out.println(Math.abs(x));
	}
}
		}catch(Exception e){
		    return;
		}
	}

}
