help with fixing translation for KN Mil 3.7.16. . Arūpa-dhamma-vavatthāna-duk-kara-pañha

I need help from some pali experts here.

First,  T.W. Rhys Davids translation of this passage, and then my attempt to fix it.

I highlight the important part that I want to get precisely correct.

T.W. Rhys Davids translation of this passage:

3.7.16. A hard thing 16. Arūpa-dhamma-vavatthāna-duk-kara-pañha

16. Arūpa-dhamma-vavatthāna-duk-kara-pañha	3.7.16. A hard thing
Rājā āha—“bhante nāgasena, dukkaraṃ nu kho bhagavatā katan”ti?	The king asked bhante, is there a difficult thing done by the Blessed one?
Thero āha— “dukkaraṃ, mahārāja, bhagavatā katan”ti.	The Elder said: ‘A hard thing there is, O king, which the Blessed One has done.’
“Kiṃ pana, bhante nāgasena, bhagavatā dukkaraṃ katan”ti.	‘And what is that?’
“Dukkaraṃ, mahārāja, bhagavatā kataṃ imesaṃ arūpīnaṃ cittacetasikānaṃ dhammānaṃ ekārammaṇe vattamānānaṃ vavatthānaṃ akkhātaṃ	‘The fixing of all those mental conditions which depend on one organ of sense, telling us that
‘ayaṃ phasso, ayaṃ vedanā, ayaṃ saññā, ayaṃ cetanā, idaṃ cittan’”ti.	such is contact, and such sensation, and such idea, and such intention, and such thought.’
“Opammaṃ karohī”ti.	‘Give me an illustration.’
“Yathā, mahārāja, kocideva puriso nāvāya mahāsamuddaṃ ajjhogāhetvā hatthapuṭena udakaṃ gahetvā jivhāya sāyitvā jāneyya nu kho, mahārāja, so puriso ‘idaṃ gaṅgāya udakaṃ, idaṃ yamunāya udakaṃ, idaṃ aciravatiyā udakaṃ, idaṃ sarabhuyā udakaṃ, idaṃ mahiyā udakan’”ti?	‘Suppose, O king, a man were to wade down into the sea, and taking some water in the palm of his hand, were to taste it with his tongue. Would he distinguish whether it were water from the Ganges, or from the Jumna, or from the Aciravatī, or from the Sarabhū, or from the Mahī?’
“Dukkaraṃ, bhante, jānitun”ti.	‘Impossible, Sir.’
“Ito dukkarataraṃ kho, mahārāja, bhagavatā kataṃ imesaṃ arūpīnaṃ cittacetasikānaṃ dhammānaṃ ekārammaṇe vattamānānaṃ vavatthānaṃ akkhātaṃ ‘ayaṃ phasso, ayaṃ vedanā, ayaṃ saññā, ayaṃ cetanā, idaṃ cittan’”ti.	‘More difficult than that, great king, is it to have distinguished between the mental conditions which follow on the exercise of any one of the organs of sense!’
“Suṭṭhu, bhante”ti rājā abbhānumodīti.	‘Very good, Nāgasena!’
Arūpadhammavavatthānadukkarapañho soḷasamo.	end of the sutta
Arūpadhammavavatthānavaggo sattamo.	Here ends the Seventh Chapter.
Imasmiṃ vagge soḷasa pañhā.	this chapter (had) 16 questions



frankk's attempt to fix passage:

3.7.16. 

16. Form-less [samadhi attainment where] Dharma [mind object inspection] - difficult - to do - questions

 16. A-rūpa-dhamma-vavatthāna-duk-kara-pañha

16. Arūpa-dhamma-vavatthāna-duk-kara-pañha	3.7.16. A hard thing
Rājā āha—“bhante nāgasena, dukkaraṃ nu kho bhagavatā katan”ti?	The king asked bhante, is there a difficult thing done by the Blessed one?
Thero āha— “dukkaraṃ, mahārāja, bhagavatā katan”ti.	The Elder said: ‘A hard thing there is, O king, which the Blessed One has done.’
“Kiṃ pana, bhante nāgasena, bhagavatā dukkaraṃ katan”ti.	‘And what is that?’
“Duk-karaṃ, mahā-rāja, bhagavatā kataṃ  imesaṃ a-rūpīnaṃ citta-cetasikānaṃ dhammānaṃ ek-ārammaṇe vattamānānaṃ va-vatthānaṃ  akkhātaṃ	‘difficult-to-do, great-king, (is what the) blessed-one has-done, this form-less (samadhi attainment where) mind -and-mental-factor dharma-objects with single-object (are seen to) exist or not-exist, (the buddha) declared:
‘ayaṃ phasso, ayaṃ vedanā, ayaṃ saññā, ayaṃ cetanā, idaṃ cittan’”ti.	such is contact, and such sensation, and such perception, and such intention, and such the-mind.’
“Opammaṃ karohī”ti.	‘Give me an illustration.’
“Yathā, mahārāja, kocideva puriso nāvāya mahāsamuddaṃ ajjhogāhetvā hatthapuṭena udakaṃ gahetvā jivhāya sāyitvā jāneyya nu kho, mahārāja, so puriso ‘idaṃ gaṅgāya udakaṃ, idaṃ yamunāya udakaṃ, idaṃ aciravatiyā udakaṃ, idaṃ sarabhuyā udakaṃ, idaṃ mahiyā udakan’”ti?	‘Suppose, O king, a man were to wade down into the sea, and taking some water in the palm of his hand, were to taste it with his tongue. Would he distinguish whether it were water from the Ganges, or from the Jumna, or from the Aciravatī, or from the Sarabhū, or from the Mahī?’
“Dukkaraṃ, bhante, jānitun”ti.	‘Impossible, Sir.’
“Ito dukkarataraṃ kho, mahārāja, bhagavatā kataṃ imesaṃ arūpīnaṃ cittacetasikānaṃ dhammānaṃ ekārammaṇe vattamānānaṃ vavatthānaṃ akkhātaṃ ‘ayaṃ phasso, ayaṃ vedanā, ayaṃ saññā, ayaṃ cetanā, idaṃ cittan’”ti.	‘More difficult than that, great king, is it to have distinguished between the mental conditions which follow on the exercise of any one of the organs of sense!’
“Suṭṭhu, bhante”ti rājā abbhānumodīti.	‘Very good, Nāgasena!’



The important grammar questions are:

what is arupa referring to here? Buddha is in an arupa samadhi to do that dharma discernement?

Or that those dharma factors being discerned (contact, perception, etc.) are -form-less arupa?

Also I'm not clear at all how all of these pieces work together in that statement:

citta-cetasikānaṃ dhammānaṃ ek-ārammaṇe vattamānānaṃ va-vatthānaṃ 

doctrinally, such as MN 111, we know this kind of dharma factor discernement can be done in 4 jhanas and first 3 arupa samadhi attainments, so I would think this passage is referring to those dharma factors are what is arupa, not that the Buddha must be in an arupa samadhi to do that.