CF1716E.Swap and Maximum Block

You are given an array of length $2^n$ . The elements of the array are numbered from $1$ to $2^n$ .

You have to process $q$ queries to this array. In the $i$ -th query, you will be given an integer $k$ ( $0 \le k \le n-1$ ). To process the query, you should do the following:

• for every $i \in [1, 2^n-2^k]$ in ascending order, do the following: if the $i$ -th element was already swapped with some other element during this query, skip it; otherwise, swap $a_i$ and $a_{i+2^k}$ ;
• after that, print the maximum sum over all contiguous subsegments of the array (including the empty subsegment).

For example, if the array $a$ is $[-3, 5, -3, 2, 8, -20, 6, -1]$ , and $k = 1$ , the query is processed as follows:

• the $1$ -st element wasn't swapped yet, so we swap it with the $3$ -rd element;
• the $2$ -nd element wasn't swapped yet, so we swap it with the $4$ -th element;
• the $3$ -rd element was swapped already;
• the $4$ -th element was swapped already;
• the $5$ -th element wasn't swapped yet, so we swap it with the $7$ -th element;
• the $6$ -th element wasn't swapped yet, so we swap it with the $8$ -th element.

So, the array becomes $[-3, 2, -3, 5, 6, -1, 8, -20]$ . The subsegment with the maximum sum is $[5, 6, -1, 8]$ , and the answer to the query is $18$ .

Note that the queries actually change the array, i. e. after a query is performed, the array does not return to its original state, and the next query will be applied to the modified array.

The first line contains one integer $n$ ( $1 \le n \le 18$ ).

The second line contains $2^n$ integers $a_1, a_2, \dots, a_{2^n}$ ( $-10^9 \le a_i \le 10^9$ ).

The third line contains one integer $q$ ( $1 \le q \le 2 \cdot 10^5$ ).

Then $q$ lines follow, the $i$ -th of them contains one integer $k$ ( $0 \le k \le n-1$ ) describing the $i$ -th query.

For each query, print one integer — the maximum sum over all contiguous subsegments of the array (including the empty subsegment) after processing the query.

Transformation of the array in the example: $[-3, 5, -3, 2, 8, -20, 6, -1] \rightarrow [-3, 2, -3, 5, 6, -1, 8, -20] \rightarrow [2, -3, 5, -3, -1, 6, -20, 8] \rightarrow [5, -3, 2, -3, -20, 8, -1, 6]$ .