Prove that for the mazes generated by the algorithm in Section 8.7, the path from the starting

Question:

Prove that for the mazes generated by the algorithm in Section 8.7, the path from the starting to ending points is unique.
α(M,N) = min{i ≥ 1| (A (i, M/N) > logN)}, where
A(1, j) = 2j............................................j ≥ 1
A(i, 1) = A(i − 1, 2) .................................i ≥ 2
A(i, j) = A(i − 1, A(i, j − 1)).....................i, j ≥ 2