SOLVE
LATER
Akash is interested in a new function F such that,
$$$F(x) = \frac{1}{GCD(1, x)} + \frac{2}{GCD(2, x)} + ... + \frac{x}{GCD(x, x)}$$$
where $$GCD$$ is the Greatest Common Divisor.
Now, the problem is quite simple. Given an array $$A$$ of size $$N$$, there are 2 types of queries:
Input:
First line of input contain integer $$N$$, size of the array.
Next line contain $$N$$ space separated integers.
Next line contain integer $$Q$$, number of queries.
Next $$Q$$ lines contain one of the two queries.
Output:
For each of the first type of query, output the required sum (mod $$10^9 + 7$$).
Constraints:
$$1 \le N \le 10^6$$
$$1 \le Q \le 10^5$$
$$1 \le A[i] \le 5 * 10^5$$
For $$1^{st}$$ type of query,
$$1 \le X \le Y \le N$$
For $$2^{nd}$$ type of query
$$1 \le X \le N$$
$$1 \le Y \le 5 * 10^5$$
$$A[1] = 3, A[2] = 4, A[3] = 3$$
$$F(3) = \frac{1}{GCD(1, 3)} + \frac{2}{GCD(2, 3)} + \frac{3}{GCD(3, 3)} = 1 + 2 + 1 = 4$$
$$F(4) = \frac{1}{GCD(1, 4)} + \frac{2}{GCD(2, 4)} + \frac{3}{GCD(3, 4)} + \frac{4}{GCD(4, 4)} = 1 + 1 + 3 + 1 = 6.$$
First query, the sum will be $$F(3) + F(4) = 4 + 6 = 10 (mod 10^9 + 7)$$.
Second query, the sum will be $$F(3) + F(4) + F(3) = 4 + 6 + 4 = 14 (mod 10^9 + 7)$$.
Third query, the sum will be $$F(3) = 4 (mod 10^9 + 7)$$.
Fourth query will update $$A[1] = 4$$.
Fifth query, the sum will be $$F(4) + F(4) + F(3) = 6 + 6 + 4 = 16 (mod 10^9 + 7)$$.
Sixth query, the sum will be $$F(4) + F(4) = 6 + 6 = 12 (mod 10^9 + 7).$$
Challenge Name
HackerEarth Collegiate Cup - First Elimination
HackerEarth Collegiate Cup - First Elimination