Howto handle reference in CustomCreationConverter (json.net)

There are two classes

public class Playlist {
    public string Name { get; set; }
    public Schedule Schedule1 { get; set; }
    public Schedule Schedule2 { get; set; }
}

public interface Schedule {
    string Name { get; set; }
}

[JsonObject(MemberSerialization = MemberSerialization.OptIn, IsReference = true)]
public class ScheduleImpl : Schedule {
    [JsonProperty]
    public string Name { get; set; }
}

each playlist has two schedules, the client code like below,

static void Main(string[] args) {
    Playlist p1 = new Playlist { Name = "playlist1" };
    p1.Schedule1 = new ScheduleImpl { Name = "schedule1" };
    p1.Schedule2 = p1.Schedule1;

    var content = Serialize(p1);
    Console.WriteLine(content);

    Console.WriteLine("----------------------------------------------------");
    Console.ReadLine();

    var p = Deserialize<Playlist>(content);
    Console.WriteLine(p.Schedule1.Name);
    Console.WriteLine(p.Schedule2.Name);

    Console.WriteLine("press any key to exit.");
    Console.ReadLine();
}

private static string Serialize(Playlist arg) {
    var settings = new JsonSerializerSettings() { NullValueHandling = NullValueHandling.Ignore };
    return JsonConvert.SerializeObject(arg, Formatting.Indented, settings);
}

private static T Deserialize<T>(string arg) {
    var settings = new JsonSerializerSettings();
    settings.Converters = new JsonConverter[] { 
        new CustomCreationConverter<Schedule, ScheduleImpl>()
    };
    return JsonConvert.DeserializeObject<T>(arg, settings);
}

the custom creation converter can't handle the reference, should I parse the 'ref' by myself?

public class CustomCreationConverter<A, T> : CustomCreationConverter<A>
    where T : A, new() {
    public override A Create(Type objectType) {
        return new T();
    }
}

and the json output is,

{
  "Name": "playlis