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.