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 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.lang.Math;
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 m = x / d;
      
      	if( Math.abs(m) > k ){
          if( m > 0 ){
          	x = x - k*d;
          }else{
            x = x + k*d;
          }
          //System.out.println(x+":"+k+":"+m);
        }else{
          x = x - m*d;
          k = k - Math.abs(m);
          //System.out.println(x+":"+k+"::"+m);
          if( k%2 == 1 ){
            if( Math.abs(x+d) <= Math.abs(x-d) ){
              x += d;
            }else{
              x -= d;
            }
          }
          
        }
      System.out.println(Math.abs(x));
	}
}