Notice that any integer can be formed by summations of powers of 2 (e.g. 0b1101 is just sum of 2^0 + 2^2 + 2^3 and so on) so you just have to find the max drop(i.e. max diff a[i] — a[j] where i < j). If max diff <= 0 then you already have a non-decreasing array so your done. If it's greater than zero, than just find the smallest x where 2^x — 1 >= max diff and you are done.

To prevent overflow. (low + high) is computed before dividing by 2 so may cause overflow.