Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

6 2 4

Sample Output 1

2

Takahashi is now at coordinate 6. It is optimal to make the following moves:

Move from coordinate 6 to (6 - 4 =) 2.

Move from coordinate 2 to (2 - 4 =) -2.

Here, the absolute value of the coordinate of the destination is 2, and we cannot make it smaller.

Sample Input 2

7 4 3

Sample Output 2

1

Takahashi is now at coordinate 7. It is optimal to make, for example, the following moves:

Move from coordinate 7 to 4.

Move from coordinate 4 to 7.

Move from coordinate 7 to 4.

Move from coordinate 4 to 1.

Here, the absolute value of the coordinate of the destination is 1, and we cannot make it smaller.

Sample Input 3

10 1 2

Sample Output 3

8

Sample Input 4

1000000000000000 1000000000000000 1000000000000000

Sample Output 4

1000000000000000

The answer can be enormous.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

class Main{

	public static void main (String[] args) {

		Main main = new Main();

		java.util.Scanner sc = new java.util.Scanner(System.in);

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

		long nowplace = X;

		if (X>0) {
			long count = X/D;
			if (X%D!=0) {
				count++;
			}
			if (count<K) {
				nowplace = X-(count*D);
				if (count==K) {
					System.out.println(Math.abs(nowplace));
				} else if ((K-count)%2==0) {
					System.out.println(Math.abs(nowplace));
				} else {
					System.out.println(Math.abs(nowplace+D));
				}
			} else {
				nowplace = X-(K*D);
				System.out.println(Math.abs(nowplace));
			}
		} else {
			long count = X/D;
			if (X%D!=0) {
				count++;
			}
			if (count<K) {
				nowplace = X+(count*D);
				if (count==K) {
					System.out.println(Math.abs(nowplace));
				}
				if ((K-count)%2==0) {
					System.out.println(Math.abs(nowplace));
				} else {
					System.out.println(Math.abs(nowplace-D));
				}
			} else {
				nowplace = X+(K*D);
				System.out.println(Math.abs(nowplace));
		}
		sc.close();
		}
	}
}