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;
public class Main{
	public static void main(String[] args){
		
      	Scanner sc = new Scanner(System.in);
      	long X = Math.abs(sc.nextLong());
     	long K = sc.nextLong(); //回数
		long D = sc.nextLong(); //移動距離
      	
      	long min_d = X % D;      
      	long req_k = X / D;
      
      	if(min_d > D / 2){
          min_d = D - min_d;
          req_k++;
        }
      
      	if(K == req_k){
        	System.out.println(min_d);
        }else if( K > req_k){
        	if((K - req_k) % 2 == 0){
            	System.out.println(min_d);
            }else{
            	System.out.println(D - min_d);
            }
        }else{
          System.out.println(X - K * D);
        }
	}
}