Creating a tree of size N in time O(lg N)

Puzzle :)

-module(foo).

-compile(export_all).

%% Create a binary tree in O(depth)
build(0, T) -> T;
build(K, T) -> build(K-1, {T, T}).

%% What is the size of such a tree
sz(X) when is_atom(X) -> 1;
sz({L, R}) ->
    1 + sz(L) + sz(R).

%% Test
test() ->
    X = this_is_an_atom,
    T = build(10, X),
    sz(T).

%% foo:test() ==> 2047 :)