2021 年东华大学金马程序设计联赛

This question is similar to Move The Numbers.

A permutation of size $2^n$ is an array of size $2^n$ such that each integer from $1$ to $2^n$ occurs exactly once in this array.

An inversion in a permutation $p$ is a pair of indices $(i,\hspace{0.17em}j)$ such that $i>j$ and $a_i\le a_j$. For example, a permutation $[4,\hspace{0.17em}1,\hspace{0.17em}3,\hspace{0.17em}2]$ contains $4$ inversions: $(2,\hspace{0.17em}1),(3,\hspace{0.17em}1),(4,\hspace{0.17em}1),(4,\hspace{0.17em}3)$.

You are given a permutation $a$ of size $2^n$ and $m$ queries to it. Each query is represented by one number $t(0\le t\le n)$ denoting that you have to reverse the segment $[1,2^t],[2^t+1,2\times 2^t],[2\times 2^t+1,3\times 2^t],\cdots ,[2^n-2^t+1,2^n]$ of the permutation.

For example, if $a\hspace{0.17em}=\hspace{0.17em}[1,\hspace{0.17em}2,\hspace{0.17em}3,\hspace{0.17em}4,5,6,7,8]$ and a query $t=1$ is applied, then the resulting permutation is $[2,1,4,3,6,5,8,7]$.

After each query you have to answer the number of inversions.