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.

Constraints

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

Examples

Input:
limit = 12
factors = [3, 5]

Expected output:
expected = 33

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

Expected output:
long long expected = 33;

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

Expected output:
long expected = 33;

Input:
limit = 10
factors = [2, 4]

Expected output:
expected = 20

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

Expected output:
long long expected = 20;

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

Expected output:
long expected = 20;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

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