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  = Math.abs(sc.nextLong());
		long k  = sc.nextLong();
		long d  = sc.nextLong();
		long ans = 0;

		//最初にできるだけ0に近づける
		long devide = x / d;
		long rest = x % d;
		
		//0に近づけるだけでk回動く場合
		if(devide >= k) {
			ans = x - (k * d);
		}else {
			
			//k - divideが偶数なら何もしない
			if((k - devide) % 2 == 0) {
				ans = rest;
			}else {
				//k - divideが奇数なら1度だけ動かす
				ans = d - rest;
			}
		}
		
		System.out.println(ans);
		sc.close();
	}
}


