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: Wrong Answer)

x,k,d=gets.split.map &:to_i
tn=[k,d].min
tx=[k,d].max
k=tn
d=tx
# 最小となる絶対値は、x<i*d以降変わらない。
# kが偶数か奇数か
=begin
while i <= k
  tmp = (x-k*i*d).abs
  if t.include?(tmp) || t.any?{ |i| tmp > i } || k <= 0
    t << tmp
    puts t.min
    break
  end
  p t << tmp
  kd = (k * d)
end
=end

t = []
k.times do |i|
  tmp = x.dup
  x = (tmp-d).abs > (tmp+d).abs ? x+d : x-d
  break if t.include?(x.abs) && (((d%2==0) && ((i+1)%2==0)) || ((d%2!=0) && ((i+1)%2!=0)))
  t << x.abs
end
puts x.abs