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.*;
import java.io.*;
import java.math.*;

class Main
{
    public static void main(String[] args) throws IOException{
        PrintWriter out = new PrintWriter(System.out);

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());

        long X = Long.parseLong(st.nextToken());
        long K = Long.parseLong(st.nextToken());
        long D = Long.parseLong(st.nextToken());

        X = Math.abs(X);
        BigInteger best = BigInteger.valueOf(X).subtract(BigInteger.valueOf(K).multiply(BigInteger.valueOf(D)));
        if (best.compareTo(BigInteger.ZERO)>=0) {
            out.println(best.longValue());
        }
        else {
            K-=X/D;
            X=X%D;
            long b = Math.abs(X-D);
            if (K%2==0) {
                out.println(X);
            }
            else
                out.println(b);
        }


        out.close();
    }

    

}
