[ICPC 2021 Macao R] Pass the Ball!

There are $n$ children playing with $n$ balls. Both children and balls are numbered from $1$ to $n$. Before the game, $n$ integers $p_1, p_2, \cdots, p_n$ are given. In each round of the game, child $i$ will pass the ball he possesses to child $p_i$. It is guaranteed that no child will pass his ball to himself, which means $p_i \neq i$. Moreover, we also know that after each round, each child will hold exactly one ball. Let $b_i$ be the ball possessed by child $i$. At the beginning of the game, child $i$ ($1 \le i \le n$) will be carrying ball $i$, which means $b_i=i$ initially. You're asked to process $q$ queries. For each query you're given an integer $k$ and you need to compute the value of $\sum\limits_{i=1}^{n} i \times b_i$ after $k$ rounds. ## Input There is only one test case for each test file. The first line of the input contains two integers $n$ ($2 \le n \le 10^5$) and $q$ ($1 \le q \le 10^5$), indicating the number of children and the number of queries. The second line contains $n$ integers $p_1, p_2, \cdots, p_n$ ($1 \le p_i \le n$) indicating how the children pass the balls around. For the following $q$ lines, the $i$-th line contains one integer $k_i$ ($1 \le k_i \le 10^9$) indicating a query asking for the result after $k_i$ rounds. ## Output For each query output one line containing one integer indicating the answer. [samples] ## Note The sample test case is explained below. $$ \begin{array}{|c|c|c|c|c|c|} \hline \textbf{Round} & \textbf{b1} & \textbf{b2} & \textbf{b3} & \textbf{b4} & \textbf{Answer} \\\hline 1 & 3 & 1 & 4 & 2 & 25 \\\hline 2 & 4 & 3 & 2 & 1 & 20 \\\hline 3 & 2 & 4 & 1 & 3 & 25 \\\hline 4 & 1 & 2 & 3 & 4 & 30 \\\hline \end{array} $$