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.Scanner;
import java.util.Arrays;

public class Main{
	public static void main(String args[]){
      Scanner scan = new Scanner(System.in);
      long X = scan.nextLong();//初期座標
      long K = scan.nextLong();//移動する回数
      long D = scan.nextLong();//一回で移動する距離
      
      X = Math.abs(X);
      long straight = Math.min(K,X / D);
      long Y = X - (straight * D);
      K -= straight;
      
      if(K > 0)
        if(K % 2 == 1)
          Y = Math.abs(Y - D);
       
      System.out.println(Y);
    }
}