Just to add another idea of how to do it...
@a=qw(1 2 3 4 5 6 7 8 9 2 3 1 4 5 6 7 8 9 1 4);
$first=3;
$last=1;
@l{@a}=0..$#a;
@f{reverse @a}=reverse 0..$#a;
print join ' ',@a[$f{$first}..$l{$last}],"\n";
This solves the problem by storing the first and last index of each number in %f and %l. Then you can get the whole slice between both numbers.
Maybe you want to use
@a[$f{$first}..$l{$last}>=$f{$first}?$l{$last}:$#a]
to get the complet rest of the array if the last number isn't behind the first.
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