blokhead's analysis sounds true. When dealing with millions of values, Perl uses up all available memory.
Since you're only using integers, one method to reduce memory usage considerably is to use a string of packed integers. Tie::IntegerArray makes this transparent for you. (It's suppose to, at least. Untested.) Use it in conjunction with blokhead's change to use a reference.
my @integer_array;
tie @integer_array, 'Tie::IntegerArray',
bits => 32,
signed => 1,
size => 1_000_000; # Pre-allocate this many
By the way, why do you switch from a binary search to a linear search to find the beginning of a match?
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