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.*;
import java.lang.Math;
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 m = x / d;
      
      	if( Math.abs(m) > k ){
          if( m > 0 ){
          	x = x - k*d;
          }else{
            x = x + k*d;
          }
          //System.out.println(x+":"+k+":"+m);
        }else{
          x = x - m*d;
          k = k - Math.abs(m);
          //System.out.println(x+":"+k+"::"+m);
          if( k%2 == 1 ){
            if( Math.abs(x+d) <= Math.abs(x-d) ){
              x += d;
            }else{
              x -= d;
            }
          }
          
        }
      System.out.println(Math.abs(x));
	}
}