There are \(N\) stalls in a vegetable market that are selling vegetables. You have to buy an equal amount of vegetables from each stall. If a stall does not have enough vegetables to offer, then you have to buy all the vegetables available in that stall. If you are given the number of vegetables that every stall can offer, determine the minimum quantity that you need to buy from each stall such that you have at least \(K\) vegetables in total.

Input format

First line: Integer \(N\) denoting the number of stalls
Next line: \(N\) space-separated integers and \(quan_{i}\) denoting the \(i^{th}\) integer which determines the quantity of vegetables that \(i^{th}\) stall would be offering
Next line: Integer \(Q\) denoting the number of queries
Next \(Q\) lines: Integer \(K_{i}\) denoting the minimum amount of vegetables needed in total

Output format

For each query, print the minimum quantity of vegetables that you have to buy from each shop in a new line. Print \(-1\) if it is not possible to buy the required number of vegetables.

Constraints

\(1 \leq N \leq 10^5\)

\(1 \leq quan_{i} \leq 10^6\)

\(1 \leq Q \leq 10^{5}\)

\(1 \leq K_{i} \leq 10^{11}\)