MEX on Ranges

You are given a $0$-indexed binary string $S$ of length $N + 1$, and your task is to construct an array $A$ of length $N$ such that: - $S_X = 1$ (for $0 \le X \le N$) if and only if there exists $L$ and $R$ such that: - $1 \le L \le R \le N$ - $MEX(A[L, R]) = X$, where $A[L, R]$ denotes the subarray $[A_L, A_{L + 1}, \ldots, A_R]$, and MEX denotes the minimum non-negative integer not pres