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.*;
import java.io.*;
import java.math.BigInteger;
 
public class Main {
	public static void main(String[] args) {
	Scanner s = new Scanner(System.in);
	long X = s.nextLong();
	long K = s.nextLong();
	long D = s.nextLong();
	
	if(Math.abs(X)/D < K){
		if((K-X/D)%2 == 0){
			System.out.println(Math.abs(X)%D);
		}else{
			System.out.println(Math.abs(Math.abs(X)%D-D));
		}
	}else{
		System.out.println(Math.abs(X)-D*K);
	}
    
  }
}