# After duplicates have been removed
# @a = ( 20, 33, 60 );
# @b = ( 2, 5, 12, 16, 23 ); 

60 / 12 = 5 / 1

# @a = ( 20, 33, 5 );
# @b = ( 2, 5, 16, 23 );

20 / 5 = 4 / 1

# @a = ( 4, 33, 5 );
# @b = ( 2, 16, 23 );

16 / 4 = 4 / 1

# @a = ( 33, 5 );
# @b = ( 2, 4, 23 );

##</code><code>##

#!/usr/bin/perl
use strict;
use warnings;
use Inline 'C';

my (%set_a, %set_b);
++$set_a{$_} for 10, 20, 33, 45, 60;
++$set_b{$_} for 2, 5, 10, 12, 16, 23, 45;

cancel_out(); # Assume %set_a and %set_b at package scope

print "$_\t$set_a{$_}\n" for keys %set_a;
print "\n\n\n";
print "$_\t$set_b{$_}\n" for keys %set_b;

sub cancel_out {
    my $finished;
    while ( ! $finished ) {
        $finished = 1;
        for ( keys %set_a ) {
            if ( exists $set_b{$_} ) {
                my $res = $set_a{$_} <=> $set_b{$_};
                if ( ! $res ) {
                    delete $set_a{$_}, delete $set_b{$_}
                }
                elsif ( $res < 0 ) {
                    $set_b{$_} -= delete($set_a{$_});
                }
                else {
                    $set_a{$_} -= delete($set_b{$_});
                }
            }
            next if ! exists $set_a{$_};
            my $m = $_;
            for my $n ( keys %set_b ) {
                my $gcd = gcd($m, $n);
                if ($gcd > 1 ) {
                    ++$set_a{$m / $gcd} if $m != $gcd;
                    ++$set_b{$n / $gcd} if $n != $gcd;
                    ! --$set_a{$m} && delete $set_a{$m};
                    ! --$set_b{$n} && delete $set_b{$n};
                    $finished = 0, last;
                }
            }
        }
    }
}
__END__
__C__

/* Implementation of Euclid's Algorithm by fizbin */
int gcd(int m, int n) {
    while( 1 ) {
        if (n==0) {return m;}
        m %= n;
        if (m==0) {return n;}
        n %= m;
    }
}