The man who kept peeing

Rajendra is a 19 year old man who for the past day has been passing urine every few minutes. He keeps drinking water, but still feels thirsty. He has also felt some generalised abdominal pain over this time and vomited twice. He has no past medical history. He says:

“I can’t stop peeing, doc”

A urine dipstick is done. This reveals:

Leucocytes +
Nitrites –
Protein Trace
Blood –
Ketones ++
Glucose ++

A capillary glucose is done which is 16.4 mmol/L. Which investigation would seal the likely diagnosis?

Venous blood gas

Arterial blood gas

HbA1c