Bessie the cow was excited to recently return to in-person learning! Unfortunately, her instructor, Farmer John, is a very boring lecturer, and so she ends up falling asleep in class often.
Farmer John has noticed that Bessie has not been paying attention in class. He has asked another student in class, Elsie, to keep track of the number of times Bessie falls asleep in a given class. There are N class periods (2≤N≤10^5), and Elsie logs that Bessie fell asleep ai times (1≤ai≤10^18) in the i-th class period. The total number of times Bessie fell asleep across all class periods is at most 1018.
Elsie, feeling very competitive with Bessie, wants to make Farmer John feel like Bessie is consistently falling asleep the same number of times in every class -- making it appear that the issue is entirely Bessie's fault, with no dependence on Farmer John's sometimes-boring lectures.
The only ways Elsie may modify the log are by combining two adjacent class periods or splitting a class period into two. For example, if a=[1,2,3,4,5], then if Elsie combines the second and third class periods the log will become [1,5,4,5]. If Elsie then chooses to split the third class period into two, the log can become any of [1,5,0,4,5], [1,5,1,3,5], [1,5,2,2,5], [1,5,3,1,5], or [1,5,4,0,5].
Given Q (1≤Q≤10^5) candidates q1,…,qQ for Bessie's least favorite number (1≤qi≤1018), for each of them help Elsie compute the minimum number of modifications to the log that she needs to perform so that all the numbers in the log become the same.
INPUT FORMAT (input arrives from the terminal / stdin):
The first line of each test case contains N, and the second contains a1,a2,…,aN. The third contains Q, followed by Q lines each containing an integer qi, a candidate for Bessie's least favorite number.
OUTPUT FORMAT (print output to the terminal / stdout):
For each qi, compute the minimum number of modifications required for Elsie to convert every entry of the log into qi, or −1 if it is impossible.
SAMPLE INPUT:
6
1 2 3 1 1 4
7
1
2
3
4
5
6
12
SAMPLE OUTPUT:
6
6
4
5
-1
4
5
Elsie needs at least four modifications to convert the log into all 3s.
1 2 3 1 1 4
-> 3 3 1 1 4
-> 3 3 1 5
-> 3 3 6
-> 3 3 3 3
It is impossible for Elsie to convert the log into all 5s, which is why the correct output for that candidate is −1.
SCORING:
In test cases 2-4, N,Q≤5000
In test cases 5-7, all ai are at most 109.
Test cases 8-26 satisfy no additional constraints.
Problem credits: Jesse Choe and Benjamin Qi