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.Scanner;

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();
			long absX = Math.abs(X);
			long absD = Math.abs(D);
            long timesk = absX/absD;
            long amari = absX%absD;
            
            if(timesk>K) {
            	System.out.println(absX-K*D);
            	return;
            }
			
            long check = (K-timesk)%2;
            
            if(check==1) {
            	System.out.println(D-amari);
            }else {
            	System.out.println(amari);            	
            }			
	}	
}