Subarray Maximums

You are given a **binary** string $S$ of length $N$. Your task is to find any permutation$^\dagger$ $P$ of $[1, N]$ that satisfies the following conditions: - For each index $i$ ($1 \le i \le N$), - If $S_i = 1$, there exists a contiguous subarray of $P$ having length $i$ whose maximum element is $i$. More formally, there must exist a pair of integers $(L, R)$ such that $1 \le L \le R \le