If they reject those terms, don't work for them.

I once built a project on those terms, and was paid about $120k for it over six months (back in 2008). The startup founder business guys who financed the project sold it to Fox for around $1M. It had gone viral. Fox put a team of 10 coders on it. They had my code but didn't fully understand it, so they wanted to hire me back. My rate was $100/hr at the time and Fox wanted to pay me half of that. I said I would consult with them at my normal rate, even though I don't like their politics.

They then sent me a contract which said that they would own all copyright to my code, and anything else I did while I was working for them. I told them there was no way I would sign that. If they wanted my help they could have it. Their people told me no.

I understand that they spent $5M trying to get my code to work on their platform before deciding to shut it down, without making any money from it at all. Too bad for them. It was a victory for me. If they had not been so greedy, they could have had their program and its programmer, too.

So in short, unless you are becoming a full-time employee of this company and everything you do at work belongs to them, you should never ever sign anything which gives them the exclusive rights to your code. You can give them the right to take it, re-sell it, modify it or whatever. But not the right to prevent you from using it.

And the most important reason for this is that everything you write will become part of your toolkit that you take forward with yourself to sell to new clients, to make it easier for you the next time you're asked. And reasonably if you are asked to do the same work again, you would write the same code again. So it is unreasonable for anyone to tell you that you cannot re-use your own work.