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.io.*;
import java.util.*;
class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();
        String s[]=bu.readLine().split(" ");
        long x=Math.abs(Long.parseLong(s[0])),k=Long.parseLong(s[1]),d=Long.parseLong(s[2]);
        long moves=x/d;
        if(moves>=k)
        {
            x-=d*k;
            sb.append(x);
        }
        else
        {
            k-=moves;
            x-=d*moves;
            k%=2;
            if(k==1) x=Math.min(Math.abs(x-d),Math.abs(x+d));
            sb.append(x);
        }
        System.out.print(sb);
    }
}