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 scan = new Scanner(System.in);

                long X = scan.nextLong();
                long K = scan.nextLong();
                long D = scan.nextLong();

                long output = 0;

                long nearZeroMoveNum = Math.abs(X) / D;

                if (K <= nearZeroMoveNum) {
                	if (X >= 0) {
                		output = Math.abs(X - D * K);
                	} else {
                		output = Math.abs(X + D * K);
                	}
                } else {
                	if (X >= 0) {
                		if ((K - nearZeroMoveNum)%2 == 0) {
                			output = Math.abs(X - D * nearZeroMoveNum);
                		} else {
                			output = Math.abs(X - D * nearZeroMoveNum - D);
                		}
                	} else {
                		if ((K - nearZeroMoveNum)%2 == 0) {
                			output = Math.abs(X + D * nearZeroMoveNum);
                		} else {
                			output = Math.abs(X + D * nearZeroMoveNum + D);
                		}
                	}
                }

                System.out.println(output);

                scan.close();

        }

}