How to insert new record into table with composite key using fluent nhibernate?

Question

NHibernate

Good day to all.
I have a Person entity.
I have the entity Program.
Each Person can have multiple Programs and each Program can have multiple Persons.
There is an entity PersonProgram.
Using Fluent NHibernate I create classes like this:

// Person
    public class Person : Entity
    {        
        public virtual Int32 Id { get; set; }
        public virtual IList<PersonProgram> Programs { get; set; }
        ...
    }
    public class PersonMap : ClassMap<Person>
    {        
        Table("Person");
        Id(p => p.Id).Column("Id");
        HasMany(p => p.Programs).KeyColumn("personID").Inverse();
        ...
    }
 
// Program
    public class Program : Entity
    {        
        public virtual Int32 Id { get; set; }
        ...
    }
    public class ProgramMap : ClassMap<Program>
    {        
        Table("Program");
        Id(p => p.Id).Column("Id");
        ...
    }
// PersonProgram
    public class PersonProgram : Entity
    {        
        public virtual Person person { get; set; }
        public virtual Program Program { get; set; }
        ...
    }
    public class PersonProgramMap : ClassMap<PersonProgram >
    {        
        Table("PersonProgram");
        CompositeId()
                .KeyReference(p => p.Person, "personID")
                .KeyReference(p => p.Program, "programID");
        ...
    }

I receive the data, everything is fine with this.
When creating a new PersonProgram instance and saving it to the database, an error pops up.

var newPersonProgram = new PersonProgram();
    
    newPersonProgram.Person = existedPerson;
    newPersonProgram.Program = existedProgram;
    ...
    using (ITransaction transaction = _session.BeginTransaction())
    {        
        _session.SaveOrUpdate(newPersonProgram); // -- ошибка, что countRow = 2, ожидается 1
        //_session.Save(newPersonProgram); -- ошибка, что countRow = 2, ожидается 1
        //_session.Merge(newPersonProgram); -- ошибка, что поле personID не может быть заполнено значением NULL
 
       transaction.Commit();
    }

On Commit, exceptions pop up that are given in the comments to each save function.
What am I doing wrong?
I understand that NHibernate is trying to generate an id, although it is already in the corresponding records, it remains only to insert them. How to be?