sub period_length { 
    my $q = shift ; 

    until ( $q % 2 ) { $q /= 2 }; 
    my $r=1; 
    # say "q:$q"; 
    for (1..$q) { 
        $r = $r * 2 % $q; 
        return $_ if $r == 1; 
        # say "r:$r" 
    } 
}