Support standard Paillier encryption and decryption?

[Jinstorm]

I noticed that in https://github.com/TNO-MPC/encryption_schemes.paillier/blob/main/src/tno/mpc/encryption_schemes/paillier/paillier.py#L505

It used a simplified version of Paillier which sets g=n+1, random value c=1, and discard the higher-order terms.

Does this encryption scheme only match the distributed partial-decryption implementation in https://github.com/TNO-MPC/protocols.distributed_keygen/blob/main/src/tno/mpc/protocols/distributed_keygen/distributed_keygen.py#L287, so that the distributed partial-decryption implementation cannot be used to decrypt ciphertext encrypted by the standard Paillier?

Also, is the proposed distributed Paillier key generation scheme limited to this simplified version or it can be directly used for the standard one?