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.*;
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 oppai = Math.abs(x/d); 
		long ans_a = Math.abs(x%d);
		long ans_b = Math.abs(Math.min(ans_a+d, ans_a-d));
		
		if(oppai >= k){
			System.out.println(Math.min(Math.abs(x-d*k), Math.abs(x+d*k)));
		}else {
			if((k-oppai)%2 == 0) {
				System.out.println(ans_a);
			}else {
				System.out.println(ans_b);
			}
		}
	}
	
	
	public static int gcd(int x,int y) {
		if(x%y == 0) {
			return y;
		}else {
			return gcd(y,x%y);
		}
	}
}