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) {
		// TODO Auto-generated method stub
		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 - k*d);
			return;
		}
		
		long remain = k - div;
		
		if(remain % 2 == 0) {
			System.out.println(x%d);
		}
		else {
			System.out.println(Math.abs(x%d - d));
		}
	}
}