Help installing light to a box with three sets of wires

[Law852]

So I removed a light without having taken a photo of the set up before and now I'm having a problem reconnecting the light.

There are two light switches controlling three lights. There is one switch (switch A) that controls the light coming from the box in question (light A) and a second light (light B). And the other switch (switch B) controls the third light (light C), which is correctly connected already.

So the problem I'm having is the box that has four set of wires coming out and that connects to light A. Currently there are three black wires grouped together, which I didn't touch. Two white wires are in one group (group w1), and another two are in a second group (group w2).

If I connect the black wire (black1) - that is in the same set as one of the white wires from group w1 - with group w2, then switch A gets power and turns on light B.

If I then connect my light's black wire with black1+group w2, and the light's white wire with group w1, switch A still only turns on light B but not light A, and switch B is receiving no power and doesn't turn on light C.

So what should I be connecting so that switch A turns on both lights A and B, and switch B turns on light C????

I've attached an image that hopefully makes this more clear.