sub hp_only_1_0_in_base_x {
  ($num,$base) = @_;
  $exp = int(log($num)/log($base));
  while ($exp) {
    $try = $base ** $exp--;
    next if ($try > $num);
    $num -= $try;
    return 0 if ($try <= $num);
  }
  return ($num > 1) ? 0 : 1
}