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);
		// 整数の入力
		long aa = sc.nextLong();
      long a = Math.abs(aa);
		// スペース区切りの整数の入力
		long b = sc.nextLong();
		long c = sc.nextLong();
		// 文字列の入力
		long d = a / c;
		if(d > b){
			System.out.println(a - b * c);
         // System.out.println(0);
		}else{
			if((b- d) % 2 == 0){
				System.out.println(a % c);
              // System.out.println(1);
			}
			else{
				System.out.println(- (a % c) + c);
              // System.out.println(2);
			}
		}
		
		
	}
}