sub binarySearch {
  my ($begin, $query, $array) = @_;

  return 0        if $query < $array->[0]        and $begin == 1;
  return $#$array if $query > $array->[$#$array] and $begin == 0;

  my ($left,$right,$prevCenter, $center) = (0, $#$array, -1);

  while(1) {
    $center = int (($left + $right)/2);

    if ($query == $array->[$center]) {
      if ($begin == 1)  {
        $center-- until $center == 0
                     or $array->[$center] != $array->[$center-1];
      } else {
        $center++ until $center == $#$array
                     or $array->[$center] != $array[$center+1];
      }
      return $center;
    }

    if ($center == $prevCenter) {
      return $right   if $begin == 1;
      return $right-1 if $begin == 0;
    }
    $right = $center if $query < $array->[$center];
    $left  = $center if $query > $array->[$center];
    $prevCenter = $center;
  }
}