Problem Statement

Yuki has \(N\) sticks, and the length of the \(i\)-th stick is \(L_i\).
The sticks can be cut freely (in the direction that divides their length), but they cannot be joined together.
Yuki wants to make sticks of the same length, and is curious about how long they can be for a given number of sticks.
Write a program that, for making \(K_1, K_2,\ldots,K_Q\) sticks of the same length, finds the maximum possible length of the sticks in each case.

Input

\(N\)
\(L_1\ L_2\ \cdots\ L_N\)
\(Q\)
\(K_1\ K_2\ \cdots\ K_Q \)

\(1 \leq N \leq 100000 = 10^5\)
\(1 \leq L_i \leq 1000000000 = 10^9\)
\(1 \leq Q \leq 100000 = 10^5\)
\(1 \leq K_i \leq 500000 = 5 \times 10^5\)

Output

On the $i$-th line, output the maximum length achievable when making $K_i$ sticks of the same length.
Your answer is considered correct if the absolute error or the relative error is at most $10^{-9}$.

Sample

2
10 20
2
3 4

10.00
6.666666666666667

5
99 88 77 66 55
5
1 10 100 1000 100000

99
33
3.807692307692307
0.384279475982533
0.003849923001540