How do you solve the Combination Sum problem?

Question presented to candidate: "Given a list of distinct positive integers candidates and a target, return every unique combination of candidates that sums to the target. Each number may be used any number of times. Code it in Python."

What a strong answer should cover:

• Backtracking with a running remaining amount: choose a candidate, recurse with remaining - x, un-choose; record when remaining is 0.
• The start index: recurse with i (reuse allowed) and never go back to smaller indices, so each combination appears once instead of in every order.
• Pruning: sort the candidates and break as soon as a candidate exceeds remaining.
• Complexity is exponential in target / smallest candidate; extra space is the recursion depth, at most target / smallest candidate.
• The variants: Combination Sum II (each number once, duplicates in input: i + 1 plus the skip rule) and counting combinations with coin-change DP.
• Python details: sorted() returns a new list (the input is left alone), record path[:], and the recursion depth is up to target / smallest candidate, which can reach the default limit of 1000 frames.

Clarifying questions expected:

• Are the candidates distinct and all positive?
• May a number be used more than once?
• Does the order of the combinations (or within a combination) matter?

Code / implementation expected: Yes — a backtracking function in Python returning list[list[int]], with the start index and the sort-and-break pruning.