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 num;
			long ret;
			
			long kirisute = x/d;
			long kiriage = (x+d-1)/d;
			
			if(k<=kirisute) {
				num = k;
				ret = x-(d*num);
				System.out.println(ret);
				return;
			}
			
			long sutedistance = x-kirisute*d;
			long agedistance = kiriage*d-x;
			
			if(sutedistance<=agedistance) {
				num = kirisute;
				
			}else {
				num = kiriage;
			}
			
			ret = Math.abs(x-num*d);
			
			if((k-num)%2==0) {
				System.out.println(ret);
			}else {
				System.out.println(Math.abs(ret-d));
			}
	    }
				
	}
	
