Let T1, T2 be 2-3-4 trees and let x be a key [in neither T1, T2], such that for each pair of keys x1 ∈ T1 and x2 ∈ T2, we have x1 < x < x2. Thus, every key in T1 is smaller than every key in T2. Devise an algorithm that constructs the union of x with these two trees. Of course, the trees T1, T2 may be of different height, and the result must be a valid 2-3-4 tree. Your algorithm should run in O(1 + |h(T1) − h(T2)|).

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