CF1605E.Array Equalizer

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.

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

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 $2$ .