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 Julia (1.4.0) (judge verdict: Wrong Answer)

function F()
  X,K,D = parse.(BigInt,split(readline()))
  if X >0
    a = Int(floor(X/D))
    if a > K
      println(abs(X-K*D))
    else
    x1 = X-a*D
    x2 = X-(a+1)*D
    if abs(x1)<abs(x2)
      x = x1
    else
      x = x2
    end
    if (K-a)%2 == 0
      println(Int(x))
    else
      if abs(x+D)>abs(x-D)
        println(abs(x-D))
      else
        println(abs(x+D))
      end
    end
    end
    
  elseif X<0
    a = Int(floor(X/D))
    if a>K
      println(abs(X+K*D))
    else
    x1 = X+a*D
    x2 = X+(a+1)*D
    if abs(x1)<abs(x2)
      x = x1
    else
      x = x2
    end
    if (K-a)%2 == 0
      println(Int(x))
    else
      if abs(x+D)>abs(x-D)
        println(abs(x-D))
      else
        println(abs(x+D))
      end
    end
    end
        
        
    
  else
    if K%2==0
      println(0)
    else
      println(D)
    end
  end
  
    
  
end
F()