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: Runtime Error)

x, k ,d = gets.chomp.split(" ").map(&:to_i)
#今いる座標
#ｋkaisuu
#d idou
x = x.abs

kyouri = x - k * d
if x > 0
    if kyori > 0
        puts kyouri
    elsif kyori == 0
        puts "0"
    elsif kyori < 0
        mae = x / d
        maekyori = x - d * mae
        usiro = x - d * (mae + 1)
        kaizuu = k - mae
        if maekyori != d
            if kaizuu % 2 == 0
                puts maekyori.abs
            else
                puts usiro.abs
            end
        elsif maekyori == d
            if kaizuu % 4 == 1 || kaizuu % 4 == 3
                puts "0"
            else
                puts maekyori.abs
            end
        end
    end
elsif x == 0
    if k % 4 == 1 || k % 3 == 3
        puts d
    else
        puts "0"
    end
end