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Split a full page into two new pages, a left, a right and a pivot element. The new pages will
each contains half of the original elements.
The pivot will be computed, depending on the place
we will inject the newly added element.
If the newly added element is in the middle, we will use it
as a pivot. Otherwise, we will use either the last element in the left page if the element is added
on the left, or the first element in the right page if it's added on the right.