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 Format:
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 Format:
Output $$$q$$$ integers — the answers to each of his $$$q$$$ questions.
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 $$$2$$$.