E. Array Equalizertime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputJeevan 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.InputThe 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.OutputOutput q integers  — the answers to each of his q questions.ExamplesInput
2
3 7
-1 5
3
1
4
3
Output
2
4
2
Input
6
2 5 4 1 3 6
-1 4 6 2 3 5
3
1
8
4
Output
10
29
9
NoteConsider 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. 
2
3 7
-1 5
3
1
4
3

2 4 2 
['binary search', 'greedy', 'implementation', 'math', 'number theory', 'sortings', 'two pointers', '*2400']