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 = Long.parseLong(sc.next());
		long k = Long.parseLong(sc.next());
		long d = Long.parseLong(sc.next());
		
		if(x < 0) {
			x *= -1;
		}
		long p = x/d;
		if(p == 0) {
			long m = d-x;
			k--;
			if(k % 2 ==0) {
				System.out.println(m);
			}
			else {
				System.out.println(d-m);
			}
			return;
		}
		
		if(p >= k) {
			System.out.println(x-d*k);
			return ;
		}
		
		long l;
		
		if(Math.abs(x - d*(p+1)) <= x-d*p) {
			k -= p+1;
			l = Math.abs(x-d*(p+1));
		}
		else {
			k -= p;
			l = x-d*p;
		}
		
		if(k % 2 == 0) {
			System.out.println(l);
		}
		else {
			System.out.println(d-l);
		}
		
		}
			
}