# Sum Multiples of Three, Five, or Seven Implement `sum_multiples(limit)`. Return the sum of all distinct positive integers strictly less than `limit` that are divisible by `3`, `5`, or `7`. An integer divisible by more than one divisor is included only once. The limit itself is never included. ## Constraints - `0 <= limit <= 10^18` - The result fits in a signed 64-bit integer for the supplied tests. - Derive an approach that does not iterate through every integer below a very large limit. ## Examples - `sum_multiples(12)` returns `40` because the included values are `3, 5, 6, 7, 9, 10`. - `sum_multiples(3)` returns `0`. ## Clarifications Explain how overlap between divisor sets is corrected and how to sum an arithmetic progression without enumerating it. ## Hints Inclusion-exclusion applies to multiples of individual divisors, pairwise least common multiples, and the three-way least common multiple. ## Extensions - Accept an arbitrary list of divisors. - Return the result modulo a positive integer. - Discuss overflow-safe intermediate arithmetic.