#
# Usage:
#   factorial($n) = 1*2*...*$n
#   factorial($m, $n) = $m*($m+1)*...*$n
#
sub factorial {
  #divide and conquer
  unshift @_, 1 if 2 != @_;
  my ($m, $n) = @_;

  if ($m < $n) {
    my $k = int($m/2 + $n/2);
    return factorial($m, $k) * factorial($k+1, $n);
  }
  else {
    return Math::BigInt->new($m);
  }
}

##</code><code>##

    return Math::BigInt->new(factorial($m, $k))->bmul(factorial($k+1,$n));

##</code><code>##

    return factorial($m, $k) * factorial($k+1, $n);

##</code><code>##

#
# Usage:
#  factorial(n) = n*(n-1)*...*1
#  factorial(n, m) = n*(n-1)*...*m
def factorial (n, m=1)
  if m < n then
    k=(m+n)/2;
    factorial(k, m) * factorial(n, k+1);
  else
    m
  end
end