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 scan = new Scanner(System.in);
		
		long x = scan.nextLong();
		long k = scan.nextLong();
		long d = scan.nextLong();
		
		long oppai = Math.abs(x/d); 
		long ans_a = Math.abs(x%d);
		long ans_b = Math.abs(Math.min(ans_a+d, ans_a-d));
		
		if(oppai >= k){
			System.out.println(Math.min(Math.abs(x-d*k), Math.abs(x+d*k)));
		}else {
			if((k-oppai)%2 == 0) {
				System.out.println(ans_a);
			}else {
				System.out.println(ans_b);
			}
		}
	}
	
	
	public static int gcd(int x,int y) {
		if(x%y == 0) {
			return y;
		}else {
			return gcd(y,x%y);
		}
	}
}
 



