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 Ruby (2.7.1) (judge verdict: Accepted)

class Problem
  attr_accessor *(?a..?z).to_a.map(&:to_sym)
  def initialize
    @x,@k,@d = gets.split.map(&:to_i)
    @a = x - k * d
    @b = x + k * d
    @i = -a / (d * 2)
    @c = calc(i)
    @j = i + 1
    @d = calc(j)
  end

  def solve
    return a.abs if a >= 0
    return b.abs if b <= 0
    if c.abs < d.abs
      return c.abs
    else
      return d.abs
    end
  end

  def calc(i)
    a + 2 * d * i
  end

  def show(ans)
    puts ans
  end
end

Problem.new.instance_eval do
  show(solve)
end