Check if each prefix forms 1..k permutation

You are given an integer array `arr` of length `n` that is a permutation of the numbers `1..n` (each number appears exactly once), but in arbitrary order. For each `k` from `1` to `n`, consider the prefix subarray `arr[0..k-1]` (the first `k` elements). Determine whether these `k` elements can be rearranged to become exactly `[1, 2, ..., k]`. Return a binary array `res` of length `n` where: - `res[k-1] = 1` if `arr[0..k-1]` can be rearranged into `[1..k]` - `res[k-1] = 0` otherwise ### Example Input: `arr = [5, 3, 1, 2, 4]` Prefixes: - `k=1`: `[5]` cannot be `[1]` → `0` - `k=2`: `[5,3]` cannot be `[1,2]` → `0` - ... (If instead using the intended example semantics that output is all ones, clarify whether the window is a *sliding window* of size `k` over the array, or specifically the *prefix* of length `k`.) ### Constraints - `1 <= n <= 2e5` (or similar) - `arr` is a permutation of `1..n` Implement an efficient algorithm (better than checking/sorting each prefix independently).