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);
		Long x=sc.nextLong();
		Long k=sc.nextLong();
		Long d=sc.nextLong();
		
		if(x<0)x*=-1;
		
		Long div=x/d;
		if(div>k) {
			System.out.println(x-d*k);
			return;
		}
		
		k-=div;
		x=x%d;
		
		long ans1=x;
		long ans2=Math.abs(x-d);
		
		if(k%2==0)System.out.println(ans1);
		else System.out.println(ans2);
		
		
	}

	
}
