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.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		long x = sc.nextLong();
		x = Math.abs(x);
		long k = sc.nextLong();
		long d = sc.nextLong();
		long div = x/d;
		long ans = 0;
		if(div>k) {
			ans = x-(k*d);
		}
		else {
			k=k-div;
			ans = x - (div*d);
			if(k%2!=0) {
				long a = ans - d;
				long b = ans + d;
				if(Math.abs(a)>Math.abs(b))
					ans = b;
				else
					ans = a;
			}

		}
		System.out.println(Math.abs(ans));
		sc.close();

	}
}
