d.pl

#!/usr/bin/perl
use strict;
use warnings;
use feature qw(:5.10);
use utf8;
use bigint;

my @combination;

my ($A, $B, $K);
{
    my $line = <STDIN>;
    ($A, $B, $K) = split(/\s/, $line);
}

my $cursor = 0;
my $result = "";

while (1) {
    if ($A == 0 or $B == 0){
        $result .= "b" x $B;
        $result .= "a" x $A;
        last;
    }
    my $n = count_pattern($A-1, $B);
    if ($n + $cursor < $K){
        $cursor += $n;
        $result .= "b";
        $B--;
    }
    else {
        $result .= "a";
        $A--;
    }
}
say $result;

sub count_pattern {
    my $a_num = shift;
    my $b_num = shift;
    return combination($a_num + $b_num, $a_num);
}
sub combination {
    my $c1 = shift;
    my $c2 = shift;
    if (!defined($combination[$c1][$c2])){
        my $numerator = 1;
        for(my $i=0;$i < $c2;$i++){
            $numerator *= $c1 - $i;
        }
        my $denominator = 1;
        for(my $i=0;$i < $c2;$i++){
            $denominator *= $c2 - $i;
        }
        $combination[$c1][$c2] = $numerator / $denominator;
    }
    return $combination[$c1][$c2];
}