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.

Problem credits: Jesse Choe and Benjamin Qi

SCORING

• In test cases 2-4, \(N,Q\le 5000\)
• In test cases 5-7, all \(a_i\) are at most \(10^9\).
• Test cases 8-26 satisfy no additional constraints.

Problem credits: Jesse Choe and Benjamin Qi

The first line of each test case contains \(N\), and the second contains
\(a_1,a_2,\ldots,a_N\). The third contains \(Q\), followed by \(Q\) lines each
containing an integer \(q_i\), a candidate for Bessie's least favorite number.

For each \(q_i\), compute the minimum number of modifications required for Elsie
to convert every entry of the log into \(q_i\), or \(-1\) if it is impossible.

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