sub fact6{
  #divide and conquer
  my $m = shift;
  my $n = @_ ? shift : $m;
  if ($m < $n) {
    my $k = int($m/2 + $n/2);
    return Math::BigInt->new(fact6($m, $k))->bmul(fact6($k+1,$n));
  }
  else {
    return Math::BigInt->new($m);
  }
}