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 Perl (5.26.1) (judge verdict: Runtime Error)

use strict;
use warnings;
use utf8;
use feature qw/say/;
use POSIX qw/floor ceil/;


sub main {
    chomp(my $line = <>);
    my ($x, $k, $d) = split(/ /, $line);
    say calc($x, $k, $d);
}

sub calc {
    my ($x, $k, $d) = @_;

    if ($x > 0) {
        my $ret = $x - $k * $d;
        return $ret if $ret > 0;
    } else {
        my $ret = $x + $k * $d;
        return -$ret if $ret < 0;
    }

    if ($x > 0) {
        my $dd = floor($x / $d);
        my $r = $x%$dd;
 
        if ($dd%2 == $k%2) {
            return $r;
        } else {
            return abs($r - $d);
        }
    } else {
        my $dd = ceil($x / $d);
        my $r = $x%$d;
 
        if ($dd%2 == $k%2) {
            return $r;
        } else {
            return abs($r - $d);
        }
    }
}

main();

1;