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 long mod(long x, long y){
    return x%y<0?x%y+(y<0?-y:y):x%y;
    }
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		long x = sc.nextLong();
        x = Math.abs(x);
		long k = sc.nextLong();       
        long d = sc.nextLong();
		long ans = 0;
        if(x/d>k){ans=x-d*k;}
        else{if((k-x/d)%2==0){ans=mod(x,d);}
            else{ans=d-mod(x,d);}
            }      
		System.out.println(ans);
	}
} 