Calculating GC content from BAM file by BED file

Dear all,

I have bedg file created from bedtools -

chr1 1  10 num_of_reads

chr1 10 20 num_of_reads

chr1 20 30 num_of_reads

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3th column is information about overlapping reads at this region. I would like to add to 4th column information about GC content in reads from my BAM file. Do you have any idea how to do that? Thank you for any help.

So result should be:

ch start stop num_of_reads cg_content