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.io.IOException;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		long X = sc.nextLong();
		long K = sc.nextLong();
		long D = sc.nextLong();
		sc.close();

		long answer = 0L;
		if(X == 0L){
			if(K % 2L == 0L){
				answer = 0L;
			} else {
				answer = D;
			}
		} else {
			if(X < 0L){
				X *= -1L;
			}
			long quotient = X / D;
			if(K < quotient){
				answer = X - (K * D);
			} else {
				long mod = X % D;
				K -= quotient;
				if(K % 2L == 0L){
					answer = mod;
				} else {
					answer = Math.abs(mod - D);
				}
			}
		}
		System.out.println(answer);
	}

}