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();
      	long ans;
      	x = Math.abs(x);
      	if(x/d > k){
          	ans = x - d*k;
        }else{
        	long e = x/d;
          	k -= e;
          	x -= e*d;
          	if(k%2 == 1) x = Math.abs(x-d);
          	ans = x;
        }
      	System.out.println(ans);
    }
}