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.io.*;
import java.util.*;
import java.util.function.*;

final class Solver {
	void solve(Supplier<String> sc) {
		long X = Long.parseLong(sc.get());
		long K = Long.parseLong(sc.get());
		long D = Long.parseLong(sc.get());
		var floor = Math.floorDiv(X, D);
		var ceil = -Math.floorDiv(-X, D);
		if (Math.abs(floor) > K) {
			System.out.println(Math.abs(X - (floor < 0 ? -1 : 1) * K * D));
			return;
		}
		var floorDistance = Math.abs(X - floor * D);
		var ceilDistance = Math.abs(X - ceil * D);
		if (Math.abs(ceil) > K) {
			System.out.println(floorDistance);
		} else if ((K - floor) % 2 == 0) {
			System.out.println(floorDistance);
		} else if ((K - ceil) % 2 == 0) {
			System.out.println(ceilDistance);
		} else {
			System.out.println(D + Math.min(floorDistance, ceilDistance));
		}
	}
}

class Main {
	public static void main(String... args) {
		System.setOut(new PrintStream(new BufferedOutputStream(System.out)));
		var reader = new BufferedReader(new InputStreamReader(System.in));
		new Solver().solve(new Supplier<>() {
			StringTokenizer line;

			public String get() {
				while (line == null || !line.hasMoreTokens()) try {
					line = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new UncheckedIOException(e);
				}
				return line.nextToken();
			}
		});
		System.out.flush();
	}
}