Given that the input file has a very large number of lines, I would try to just process the file line by line (no slurping the file into a single $file_content or @lines).
Here is one way:
$cur_num = $1 if (/^(\d+)/); # new $cur num if line starts
# with digits
s/(\S+)$/$cur_num/; # substitute the non-spaces at the end
# of the line with the cur_num
print; #a blank line is not modified
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