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 PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php
// Your code here!
    $input_array = explode(" ",fgets(STDIN));
    
    $x = $input_array[0];
    $k = $input_array[1];
    $d = $input_array[2];
  
    $temp_numbers = array();
    for($i=1;$i<=$k;$i++){
        $plus = $x+$d;
        $minus = $x-$d;
        if(abs($plus)<=abs($minus)){
            $x=$x+$d;
        }else{
            $x=$x-$d;
        }
        if(abs($x)<$d/2){
            if(($k-$i)%2==0){
                break;
            }else{
                if($x<=0){
                    $x = $x+$d;
                    break;
                }else{
                    $x = $x-$d;
                    break;
                }
            }
        }
    }
    
    if($x<0){
        $x = -1 * $x;
    }
    echo $x;
     
?>