Values that appear once

Find all integers that occur exactly once in a list, preserving original order.

counting filtering order

Write a function `singles(nums)` that takes a list of integers `nums` and returns a new list containing only the integers that occur exactly once in `nums`, preserving the order of first appearance.

- The input list may be empty.
- The order of the output must match the order in which the numbers first appear in the input.
- Do not modify the input list.

**Input**
- `nums`: a list of integers (can be empty, can contain duplicates).

**Output**
- A list of integers that appear exactly once in `nums`, in their original order of first appearance.

**Complexity note**: Aim for O(n) time using a counting dictionary or set-based approach.

Constraints

- `0 <= len(nums) <= 10^5`
- Each integer fits in Python's `int` (unbounded).
- Time complexity: O(n), Space complexity: O(n) where n = len(nums).

Example

```python
>>> singles([1, 2, 3, 1, 2])
[3]
>>> singles([4, 4, 5, 6, 6, 7])
[5, 7]
>>> singles([])
[]
>>> singles([9, 9, 9])
[]
```

10 points ~15 min

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Hints

Count how many times each number appears using a dictionary.

After counting, iterate through the original list and keep the first occurrence of each number whose count is exactly one.

To preserve order, avoid using a set for the final result; instead, build a list while iterating.

You can use `collections.Counter` to simplify counting.

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