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.awt.*;
import java.io.*;
import java.net.StandardSocketOptions;
import java.util.*;

public class Main {
    Scanner sc = new Scanner(System.in);
    public static void main(String[] args){
        new Main();
    }
    public Main(){
        new TestC().doIt();
    }
    class TestC{
        void doIt() {
            long X = sc.nextLong();
            long K = sc.nextLong();
            long D = sc.nextLong();
            X = Math.abs(X);
            long Straight = Math.min(K, X/D);
            K -= Straight;
            X -= Straight * D;

            if(K % 2 == 0){
                System.out.println(X);
            }else{
                System.out.println(D - X);
            }
        }
    }
}