교실에서 잠자기2 (Sleeping in Class) timer 2s memory 1024MB

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\le N\le 10^5), and Elsie logs that Bessie fell asleep a_i times (1\le a_i\le 10^{18}) in the i-th class period. The total number of times Bessie fell asleep across all class periods is at most 10^{18}.

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\le Q\le 10^5) candidates q_1,\ldots,q_Q for Bessie's least favorite number (1\le q_i\le 10^{18}), 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.