A8734 | Naughty Stone Piles

There are $n$ piles of stones of sizes $a_{1},a_{2},...,a_{n}$ lying on the table in front of you.

During one move you can take one pile and add it to the other. As you add pile $i$ to pile $j$ , the size of pile $j$ increases by the current size of pile $i$ , and pile $i$ stops existing. The cost of the adding operation equals the size of the added pile.

Your task is to determine the minimum cost at which you can gather all stones in one pile.

To add some challenge, the stone piles built up conspiracy and decided that each pile will let you add to it not more than $k$ times (after that it can only be added to another pile).

Moreover, the piles decided to puzzle you completely and told you $q$ variants (not necessarily distinct) of what $k$ might equal.

Your task is to find the minimum cost for each of $q$ variants.

The first line contains integer $n$ $(1<=n<=10^{5})$ — the number of stone piles. The second line contains $n$ space-separated integers: $a_{1},a_{2},...,a_{n}$ $(1<=a_{i}<=10^{9})$ — the initial sizes of the stone piles.

The third line contains integer $q$ $(1<=q<=10^{5})$ — the number of queries. The last line contains $q$ space-separated integers $k_{1},k_{2},...,k_{q}$ $(1<=k_{i}<=10^{5})$ — the values of number $k$ for distinct queries. Note that numbers $k_{i}$ can repeat.

Print $q$ whitespace-separated integers — the answers to the queries in the order, in which the queries are given in the input.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.