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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

    public static void main(String[] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String []line = br.readLine().split(" ");

        long curr = Long.parseLong(line[0]), moves = Long.parseLong(line[1]), d = Long.parseLong(line[2]);

        curr=Math.abs(curr);

        long maxMoves = (long)curr/d;

        if(maxMoves > moves){
            curr-= moves*d;
            moves=0;
        }
        else {
            curr-= maxMoves*d;
            moves-= maxMoves;
        }

        if(moves >0){
            if(moves%2 == 0){
                System.out.println(Math.abs(curr));
            }
            else {
                if(Math.abs(curr-d) <= Math.abs(curr+d)){
                    System.out.println(Math.abs(curr-d));
                }
                else {
                    System.out.println(Math.abs(curr+d));
                }
            }
        }
        else {
            System.out.println(Math.abs(curr));
        }
    }
}