Sum of Multiples

Consider positive integers strictly below limit. Include a value if it is divisible by at least one nonzero factor. Count each included value once even if several factors divide it. Ignore zero factors. Factors [3, 5] give the familiar multiples-of-3-or-5 task.

Implement sum_of_multiples(limit, factors).

Input

limit: The exclusive upper bound.

factors: The factors whose multiples are eligible.

Output

Return the sum of distinct eligible positive integers.

제약 조건

0 ≤ limit ≤ 100,000. There may be 0 through 20 factors, each between 0 and 100,000. Duplicate factors are allowed.

예시

입력:
limit = 12
factors = [3, 5]

예상 출력:
expected = 33

입력:
long long limit = 12;
std::vector<long long> factors = {3, 5};

예상 출력:
long long expected = 33;

입력:
long limit = 12;
long[] factors = new long[] {3, 5};

예상 출력:
long expected = 33;

입력:
limit = 10
factors = [2, 4]

예상 출력:
expected = 20

입력:
long long limit = 10;
std::vector<long long> factors = {2, 4};

예상 출력:
long long expected = 20;

입력:
long limit = 10;
long[] factors = new long[] {2, 4};

예상 출력:
long expected = 20;

참고 자료

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• #1 Multiples of 3 or 5
• Sum of Multiples