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.InputStreamReader;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        long X = Math.abs(scan.nextLong());
        long K = scan.nextLong();
        long D = scan.nextLong();
        if (K <= X / D) {
            long ans = X - K * D;
            System.out.println(ans);
            return;
        }
        // 可能性
        long min1 = Math.abs(X - (X / D) * D);
        long remain1 = K - X / D;
        if (remain1 % 2 == 0) {
            System.out.println(min1);
            return;
        }
        long min2 = Math.abs(X - ((X / D) + 1) * D);
        long remain2 = K - X / D - 1;
        if (remain2 % 2 == 0) {
            System.out.println(min2);
            return;
        }
        throw new RuntimeException("NG");

    }
}
