3'UTR seq extraction

[leo2017]

Hello,
I am new to the forum and this is my first post here !

I have a pair of fasta sequence files one having several CDS sequences (file X) and the other with several full length transcript sequences (file Y).
The file (file X) with CDS sequence have entries as follows:
>ABCD (40..120)
…………the sequence……………….
This goes on for another 200 different gene entries

The file (file Y) with the full length transcript sequence have entries as follows:
>ABCD (1..700)
…………the sequence……………….
And this also goes on for another 200 different gene entries.

The ABCD implies a gene name which is of course identical in both the fasta files. Hence the sequence is also identical in between coordinates 40..120 for both sets.
I want to extract the 3’ UTR sequences from all the fasta sequence entries that are in the full transcript file. So basically, I am trying to come up with a script that will allow me to extract the sequence from the full transcript file right after where the CDS sequence ends. So in the above example I am trying to get the sequence between (121 ..700) for gene ABCD from the full transcript fasta file. I am trying to make the script so that it loops through the entire file for all the 200 gene entries.

I am primarily using bash and little of perl.
Any help will be most appreciated.

Thanks and regards!