Fewest Terms to Write an Integer as 1, 2 or 3 Plus Even Powers of Two

You are given an integer array `nums`. For each value `x` in `nums`, find the smallest positive integer `k` such that `x` can be written as the sum of exactly `k` integers where: - exactly one of the `k` integers is `1`, `2` or `3`, and - each of the other `k - 1` integers is a power of two whose exponent is even and at least `2`, that is, one of `4`, `16`, `64`, `256`, `1024`, and so on. The power `2^0 = 1` is not allowed for these terms. If no such `k` exists for `x`, the answer for `x` is `-1`. Return the answers as a list in the same order as `nums`. ### Function Signature ```python def min_split_terms(nums: list[int]) -> list[int]: ``` ### Rules - The same power of two may appear any number of times among the `k - 1` terms. - `k = 1` is allowed. The sum then consists of the single small term, so this applies only when `x` itself is `1`, `2` or `3`. - The order of the terms does not matter; only the count `k` is returned. - Every value in `nums` is answered independently of the others. ### Constraints - `1 <= len(nums) <= 100000` - `1 <= nums[i] <= 1000000000` - The output has the same length as `nums`. Each element is `-1` or a positive integer, and it is uniquely determined by the input. ### Examples **Example 1** - Input: `nums = [1, 5, 4, 23, 14]` - Output: `[1, 2, -1, 3, 4]` - Explanation: `1` is itself a small term, so `k = 1`. `5 = 1 + 4`. For `4`, the small term would be `1`, `2` or `3`, leaving `3`, `2` or `1` for the other terms, and none of those can be a sum of terms that are each at least `4`, so the answer is `-1`. `23 = 3 + 4 + 16`. `14 = 2 + 4 + 4 + 4`, and no choice with fewer terms reaches `14`. **Example 2** - Input: `nums = [3, 63]` - Output: `[1, 7]` - Explanation: `3` is a small term on its own. `63 = 3 + 16 + 16 + 16 + 4 + 4 + 4`, and no choice with fewer than seven terms reaches `63`.