Problem:
Score : 200 points

Problem Statement

You are given positive integers A and B.

Find the K-th largest positive integer that divides both A and B.

The input guarantees that there exists such a number.

Constraints

All values in input are integers.

1 \leq A, B \leq 100

The K-th largest positive integer that divides both A and B exists.

K \geq 1

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the K-th largest positive integer that divides both A and B.

Sample Input 1

8 12 2

Sample Output 1

2

Three positive integers divides both 8 and 12: 1, 2 and 4.
Among them, the second largest is 2.

Sample Input 2

100 50 4

Sample Output 2

5

Sample Input 3

1 1 1

Sample Output 3

1

Solution in Perl (v5.18.2) (judge verdict: Accepted)

my $input = <>;
my ($A, $B, $K) =  split(' ', $input);

my $A_yakusu = get_yakusu($A);
my $B_yakusu = get_yakusu($B);

my @koyakusu = ();
for my $num (keys %{$A_yakusu}) {
    push @koyakusu, $num if exists $B_yakusu->{$num};
}

my @sorted = sort {$a <=> $b } @koyakusu;
print $sorted[-$K];

sub get_yakusu {
    my $number = shift;

    my $hash = {};
    for my $num ( 1.. $number ) {
        $hash->{$num} = 1 if $number % $num == 0;
    }
    return $hash;
}