Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

6 2 4

Sample Output 1

2

Takahashi is now at coordinate 6. It is optimal to make the following moves:

Move from coordinate 6 to (6 - 4 =) 2.

Move from coordinate 2 to (2 - 4 =) -2.

Here, the absolute value of the coordinate of the destination is 2, and we cannot make it smaller.

Sample Input 2

7 4 3

Sample Output 2

1

Takahashi is now at coordinate 7. It is optimal to make, for example, the following moves:

Move from coordinate 7 to 4.

Move from coordinate 4 to 7.

Move from coordinate 7 to 4.

Move from coordinate 4 to 1.

Here, the absolute value of the coordinate of the destination is 1, and we cannot make it smaller.

Sample Input 3

10 1 2

Sample Output 3

8

Sample Input 4

1000000000000000 1000000000000000 1000000000000000

Sample Output 4

1000000000000000

The answer can be enormous.

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Accepted)

(let* ((n (abs (read)))
       (m (read))
       (l (read))
       (mn1 (mod n l))
       (mn1a (floor n l))
       (mn2 (- mn1 l))
       (mn2a (1+ (floor n l))))
  (if (if (= mn1 (min (abs mn1) (abs mn2)))
          (<= m mn1a)
          (<= m mn2a))
      (princ (- n (* m l)))
      (let* ((k (if (= mn1 (min (abs mn1) (abs mn2)))
                    (- m mn1a)
                    (- m mn2a))))
        (if (evenp k)
            (princ (abs (if (= mn1 (min (abs mn1) (abs mn2)))
                            mn1 mn2)))
            (princ (abs (if (= mn1 (min (abs mn1) (abs mn2)))
                            mn2 mn1)))))))