Detachments / Command Points Query

So my question is, when Building a Battle Forged Army you build an army comprised of detachments and specific detachments give you Command Points. So if I start the build with a Battalion Detachment I would get 3 CP so long as I had 3 HQ & 3 Troops choices minimum. Then I add a Vanguard Detachment, which is 1 HQ & 3 Elite. Now the question that springs to mind is, do the previously selected HQ count as an HQ choice for the Vanguard Detachment or does the Vanguard require its own HQ making 4 in total? Given the cost of HQ options in the Craftworld Codex it's going to be difficult to build a reasonable sized force and get CP's in anything 1500 or less, which is what they game around my way.

For those of you who are interested, I got a response from the Warhammer Shop website. They say that each detachment has its own discrete HQ so I would need to select an HQ option for the Vanguard detachment, which would make 4 HQ's up to that point in the Battle Forged army. The upside is, no HQ limits anymore, even in tournament play by the looks of it. The down side is, points cost my limit the CP you can acquire as you may like a secondary detachment but can't field it in its entirety.

I'm pretty sure the Battalion only requires 2+ HQs, so you can squeeze the third into your vanguard detachment.

But generally, I agree, at 1.5k it's pretty hard to get more than one detachment going.