C - Walking Takahashi

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.

6 2 4

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.

7 4 3

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.

10 1 2

8

1000000000000000 1000000000000000 1000000000000000

1000000000000000

The answer can be enormous.