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.

Examples

Input

6 2 4


Output

2


Input

7 4 3


Output

1


Input

10 1 2


Output

8


Input

1000000000000000 1000000000000000 1000000000000000


Output

1000000000000000
import java.util.*;
public class Main {
    public static void main(String[] args){
      // 入力
      Scanner sc = new Scanner(System.in);
      long X = sc.nextLong();
      long K = sc.nextLong();
      long D = sc.nextLong();
      
      // 算出
      long absX = Math.abs(X);
      long div = absX / D;
      long min1 = absX % D;
      long min2 = Math.abs(min1 - D);
      
      long result = 0L;
      if(K < div){
        result = absX - D * K;
      }else{
        if(div % 2 == 1){
          if(K % 2 == 1){
            result = min1;
          }else{
            result = min2;
          }
        }else{
          if(K % 2 == 0){
            result = min1;
          }else{
            result = min2;
          }
        }
      }
      
      // 出力
      System.out.println(result);
    }

}