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.io.*;
class Main{
	public static void main(String[]args){
		Scanner in=new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out, true);
		long x = Math.abs(in.nextLong());
		long k = in.nextLong();
		long d = in.nextLong();

		long step = Math.min(k, x/d);
		k = k - step;
		long pos = x - (step * d);
		if(k == 0){
			out.println(Math.abs(pos));
		}
		else{
			if(k % 2 == 0)
				out.println(pos);
			else
				out.println(Math.abs(pos - d));
		}
	}
}
