std::set's lower_bound() is optimized better than the generic
implementation of std::lower_bound()
std::lower_bound() works best on random access iterators, where the
number of comparisons can be logarithmic. However, since std::set's
iterators are bidirectional iterators, the comparisons will actually be
linear in practice when using std::lower_bound().
So, we can use std::set's version which is guaranteed to be logarithmic.