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.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
class Main {
  public static void main(String[] args) {
    try {
        var stdin = new BufferedReader(new InputStreamReader(System.in));
        String line = null;
        while((line = stdin.readLine()) == null);
        var parsed = line.split(" ");
        Long X = Long.valueOf(parsed[0]);
        Long K = Long.valueOf(parsed[1]);
        Long D = Long.valueOf(parsed[2]);
        
        Long sho = Math.abs(X) / D; // まず取りきる回数

        
        Long joyo = Math.abs(X) % D; // 半端数
        Long sign = X >= 0L ? 1L : -1L; //初期場所の符号
        Long maybemin = sign * joyo; // 最小値候補。半端数は符号を無視したので符号を戻してやる
        
                // とりきれなければ分かりやすい
        if (sho > K) {
            System.out.println(Math.abs(X - sign * D * K));
            return;
        }
        
        if ((K - sho) %2 == 0) { // 残り回数が偶数ならそのまま出す
            System.out.println(Math.abs(maybemin));
        } else {
            // 奇数なら最小値候補の符号と逆に動かす。最小値候補
            System.out.println(Math.abs(maybemin - sign * D));
        }
    } catch(Exception e) {
    }
   
  }
}