Determine the maximal length $L$ of a sequence $a_{1}, \\ldots, a_{L}$ of positive integers satisfying both the following properties: - every term in the sequence is less than or equal to $2^{2023}$, and - there does not exist a consecutive subsequence $a_{i}, a_{i+1}, \\ldots, a_{j}$ (where $1 \\leqslant i \\leqslant j \\leqslant L$ ) with a choice of signs $s_{i}, s_{i+1}, \\ldots, s_{j} \\in\\{1,-1\\}$ for which $$s_{i} a_{i}+s_{i+1} a_{i+1}+\\cdots+s_{j} a_{j}=0$$ Please provide the sum of the base and exponent used in the expression for the maximal length $L$. 

Let's think step by step and output the final answer within \boxed{}.
user