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: Accepted)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		long x = sc.nextLong();
		long k = sc.nextLong();
		long d = sc.nextLong();
		long min1 = x % d;
		if(min1 < 0)
			min1 += d;
		long min2 = min1 - d;
		long ans = Long.MAX_VALUE / 2;
		long sa1 = Math.abs(x - min1) / d % 2;
		if(sa1 < 0)
			sa1 += 2;
		long sa2 = Math.abs(x - min2) / d % 2;
		if(sa2 < 0)
			sa2 += 2;
		if(Math.abs(x - min1) / d <= k && sa1 == k % 2) {
			ans = Math.abs(min1);
		}
		if(Math.abs(x - min2) / d <= k && sa2 == k % 2) {
			ans = Math.abs(min2);
		}
		long ans2 = 0;
		if(x >= 0) {
			ans2 = Math.abs(x - k * d);
		}
		else {
			ans2 = Math.abs(x + k * d);
		}

		ans = Math.min(ans, ans2);


		sc.close();
		System.out.println(ans);

	}
}