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.chomp.split(' ').map(&:to_i)
all = [[x]]
# p all[0]
# p all[0][0]
min = x
i = 0
while i < k
  a = []
  j = 0
  while j < all[i].size
    a << (all[i][j]+d) if (all[i][j]+d).abs < min
    a << (all[i][j]-d) if (all[i][j]-d).abs < min
    min = all[i][j]+d if (all[i][j]+d).abs < min
    min = all[i][j]-d if (all[i][j]-d).abs < min
    # a << (all[i][j]+d)
    # a << (all[i][j]-d)
    j += 1
  end
  all << a
  i += 1
end
p min