Coins - Practice, Medium NZEC Ruby

I am getting an NZEC on this solution. I can’t figure out what could be the problem. I have read that Ruby handles large numbers dynamically and I do not need BigNum for this.
My solution link is here, any help will be very much appreciated.
link to my solution

Actually I don’t know Ruby …The best help I can provide you is that in this problem you need Dynamic Programming implementation…If you are programming in C , C++ , python , Java …Do comment , I can help you then

In C, how can you store all the possible values of n till 1,000,000,000?
How would you do it in C?

use unsigned long int for c

Use long int and if you want to be on safe side like for addition or multiplication you may use long long int that has a range of -2^64 -1 to 2^64 -1