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 scan = new Scanner(System.in);
    String str_scan = scan.nextLine();
    // スペース区切りで分ける
    var str = str_scan.split(" ");
    // int型へ変換
    var X = Long.parseLong(str[0]);
    var K = Long.parseLong(str[1]);
    var D = Long.parseLong(str[2]);

    long ans = 0;
    long syou = 0;
    long amari = 0;

    if ( X < 0 ){
      X = X * -1;
    }

    syou = X / D;
    amari = X % D;

    if ( syou < K ) {
      if ((K % 2 == 1) && (syou % 2 == 1)){
        ans = amari;
      } else if ( (K % 2 == 0) && (syou % 2 == 0)) {
        ans = amari;
      } else if ( (K % 2 == 0) && (syou % 2 == 1)) {
          ans = amari - D;
      } else if ( (K % 2 == 1) && (syou % 2 == 0)){
          ans = amari - D;
      }
      if (ans < 0) {
        ans = -1 * ans;
      }
    } else {
      ans = amari + ((syou-K) * D);
    }

    System.out.println(ans);
    scan.close();
  }
}