sub binomial {
    my ($n,$s)=@_;
    $_[1]<=$_[0]/2
        ? $_[1]
            ? 0 | ($_[0] - $_[1] + 1) * binomial( $_[0], $_[1] - 1) / $_[1]
            : 1
        : $_[1] != $_[0]
            ? 0 | ($_[1] + 1) * binomial( $_[0], $_[1] + 1) / ($_[0] - $_[1])
            : 1;
}