Array Equalizer

2000ms

262144K

Description:

Jeevan has two arrays $$$a$$$ and $$$b$$$ of size $$$n$$$. He is fond of performing weird operations on arrays. This time, he comes up with two types of operations:

Choose any $$$i$$$ ($$$1 \le i \le n$$$) and increment $$$a_j$$$ by $$$1$$$ for every $$$j$$$ which is a multiple of $$$i$$$ and $$$1 \le j \le n$$$.
Choose any $$$i$$$ ($$$1 \le i \le n$$$) and decrement $$$a_j$$$ by $$$1$$$ for every $$$j$$$ which is a multiple of $$$i$$$ and $$$1 \le j \le n$$$.

He wants to convert array $$$a$$$ into an array $$$b$$$ using the minimum total number of operations. However, Jeevan seems to have forgotten the value of $$$b_1$$$. So he makes some guesses. He will ask you $$$q$$$ questions corresponding to his $$$q$$$ guesses, the $$$i$$$-th of which is of the form:

If $$$b_1 = x_i$$$, what is the minimum number of operations required to convert $$$a$$$ to $$$b$$$?

Help him by answering each question.

Input:

The first line contains a single integer $$$n$$$ $$$(1 \le n \le 2 \cdot 10^{5})$$$ — the size of arrays $$$a$$$ and $$$b$$$.

The second line contains $$$n$$$ integers $$$a_1, a_2, ..., a_n$$$ $$$(1 \le a_i \le 10^6)$$$.

The third line contains $$$n$$$ integers $$$b_1, b_2, ..., b_n$$$ $$$(1 \le b_i \le 10^6$$$ for $$$i \neq 1$$$; $$$b_1 = -1$$$, representing that the value of $$$b_1$$$ is unknown$$$)$$$.

The fourth line contains a single integer $$$q$$$ $$$(1 \le q \le 2 \cdot 10^{5})$$$ — the number of questions.

Each of the following $$$q$$$ lines contains a single integer $$$x_i$$$ $$$(1 \le x_i \le 10^6)$$$ — representing the $$$i$$$-th question.

Output:

Output $$$q$$$ integers — the answers to each of his $$$q$$$ questions.

Sample Input:

Sample Output:

2
4
2

Sample Input:

6
2 5 4 1 3 6
-1 4 6 2 3 5
3
1
8
4

Sample Output:

10
29
9

Note:

Consider the first test case.

$$$b_1 = 1$$$: We need to convert $$$[3, 7] \rightarrow [1, 5]$$$. We can perform the following operations:
$$$[3, 7]$$$ $$$\xrightarrow[\text{decrease}]{\text{i = 1}}$$$ $$$[2, 6]$$$ $$$\xrightarrow[\text{decrease}]{\text{i = 1}}$$$ $$$[1, 5]$$$
Hence the answer is $$$2$$$.
$$$b_1 = 4$$$: We need to convert $$$[3, 7] \rightarrow [4, 5]$$$. We can perform the following operations:
$$$[3, 7]$$$ $$$\xrightarrow[\text{decrease}]{\text{i = 2}}$$$ $$$[3, 6]$$$ $$$\xrightarrow[\text{decrease}]{\text{i = 2}}$$$ $$$[3, 5]$$$ $$$\xrightarrow[\text{increase}]{\text{i = 1}}$$$ $$$[4, 6]$$$ $$$\xrightarrow[\text{decrease}]{\text{i = 2}}$$$ $$$[4, 5]$$$
Hence the answer is $$$4$$$.
$$$b_1 = 3$$$: We need to convert $$$[3, 7] \rightarrow [3, 5]$$$. We can perform the following operations:
$$$[3, 7]$$$ $$$\xrightarrow[\text{decrease}]{\text{i = 2}}$$$ $$$[3, 6]$$$ $$$\xrightarrow[\text{decrease}]{\text{i = 2}}$$$ $$$[3, 5]$$$
Hence the answer is $$$2$$$.

Informação

Provedor Codeforces

Código CF1605E