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 InputLine
  def self.to_s
    gets.chomp
  end

  def self.to_i
    InputLine.to_s.to_i
  end
  
  def self.to_f
    InputLine.to_s.to_f
  end

  def self.to_sa
    InputLine.to_s.split(' ')
  end

  def self.to_ia
    InputLine.to_sa.map(&:to_i)
  end
  
  def self.to_fa
    InputLine.to_sa.map(&:to_f)
  end
end

def f(x, k, d, i)
  (x - k * d) + 2 * d * i
end

def main(argv)
  (x, k, d) = InputLine.to_ia

  hi = k + 1
  lo = 0
  while hi - lo > 4 do
    dist = (hi - lo) / 3
    midL = lo + dist
    midR = hi - dist

    valL = f(x, k, d, midL).abs
    valR = f(x, k, d, midR).abs

    if valL < valR then
      hi = midR
    else
      lo = midL
    end
  end

  lb = [0, lo - 10].max
  ub = [k, hi + 10].min
  mval = 1e+18.to_i
  (lb..ub).each do |i|
    mval = [mval, f(x, k, d, i).abs].min
  end
  puts mval.to_s
end

if self.to_s == 'main' then
  main(ARGV)
end