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: Time Limit Exceeded)

(let ((x (read))
    (k (read))
    (l 0)
    (ki 0)
    (gu 0)
    (nokori 0)
    (dr (read)))
    (loop for i below k do
        (progn
        (if (<= x 0)
            (incf x dr)
            (decf x dr)
        )
        (if (<= i 2)
            (if (zerop (rem i 2))
                (if (= x gu)
                    (progn
                        (setq nokori (- k i 1))
                        (return)
                    )
                    (setq gu x)
                )
                (if (= x ki)
                    (progn
                        (setq nokori (- k i 1))
                        (return)
                    )
                    (setq ki x)
                )
            )
        )
        )
    )
    (if (zerop (rem nokori 2))
        (princ (abs x))
        (if (<= x 0)
            (princ (abs (+ x dr)))
            (princ (abs (- x dr)))
        )
    )
)