publications - My work was published before me. What should I do?

Some time ago I switched departments within the same institution. Before leaving I had an idea of a paper and started to work on it. I shared my thoughts on it with my then-coworkers and they praised it. So now, after I settled things in a new department, I continued to work on that paper and completed it. Before submitting anywhere, I decided to look for a new papers relevant to my work.

To my surprise, I have found a paper with my idea (implemented in a somewhat narrower sense) by several of my previous coworkers, with whom I have discussed it. Without my name on the paper of course. The paper was published a few month after I left, so they probably started to work on it immediately after I left.

Most (if not all) conversations were done verbally, so I don't have any proof that I am the original author, and I also don't know any authority that I can go to and explain the issue.

What bothers me is if I publish the paper now (even in a broadened version of it) it would look suspicious to an external observer, as if we (together with ex-coworkers) are trying to overuse and multiply a single result or even worse that I'm plagiarizing over their work. As we are in the same institution and had previously coauthored some works, nobody will believe similar papers are a coincidence or a an independent inventions. (And they would be right. It's not.) I think that in the worst case it can destroy my reputation and career, or maybe it's a non-issue and I'm worrying too much.

I can see several possible extensions and further research paths to the paper. But if I'll try to develop these ideas and publish an advanced version of the paper, there is no guarantee that they aren't doing the same. They could even had already submitted them somewhere. And if I submit my version, the reviewers may reject it because of its similarity to theirs. This again can be devastating to me.

What options I have, as I see it:

1. Pretend I don't know about their work, and publish mine as fully original, without citing them. Even if it's still a more general view on the subject and I know I'm the original author, it doesn't seem ethical to me. And we're still in the same institution, what make things worse.


2. Do more research, make more advanced paper and cite them accordingly. But they may even have submitted an advanced version somewhere. I can't be sure if I'm overlapping with them or not.


3. Change the field of study completely to not overlap with them in the future. Seems to be an overreaction.


4. Change the institution and then publish. Will it help? I'd still be their co-author-in-the-past. Seems not to be a solution at all.


5. Mention them in the acknowledgements. Thank them for praising my work, and cite them through a footnote. After all, what acknowledgements are for if not to thank your colleagues? But I doubt any editor will let it pass.

TL;DR Several of my ex-coworkers rushed to publish my ideas as their own while I was working on these ideas. I worry that my future publications on the theme would overlap with theirs and be considered a plagiarism.

So what should I do? Am I right that my wrong actions could possibly damage my reputation and career?

UPD. Thank you for your answers, I see that I have to cite the paper by the old department researchers (still not sure how: through a regular citation or a footnote in the acknowledgements), but I'm not really convinced and just want to be sure that I would not get into any (more) trouble if I'll continue to do research on the topic (especially in the case when editor/reviewers will get similar papers from different people with the same affiliation). Maybe someone has had such an experience as a reviewer?