Why the Cows Climbed onto the Information Island

$N$ cows have climbed onto the Information Island!

The cows are resting in the front yard on the first floor of the Information Island, sitting in a circle in the order $A_1, A_2, A_3, \dots, A_N, A_1$. Each cow has a sticker with a quality score $A_i$ on it. Next to the herd, Ukje found a formula that Hyobin had worked out, and it looks like this.

$S = \sum_{i=1}^N(A_{i}\times A_{i+1}\times A_{i+2}\times A_{i+3})$ (where $A_{N+1}=A_{1}, A_{N+2}=A_{2}, A_{N+3}=A_{3}$)

In words, for the cows sitting in a circle, it is the sum of the products of the quality scores of every four consecutive cows.

Ukje plans to be mean so that Hyobin cannot leave school. Over $Q$ rounds, Ukje will pick some $i$-th cow. Then he will peel off the sticker with $A_i$ and stick on a sticker with $A_i \times -1$. Hyobin then has to recompute $S$ $Q$ times. A sticker stays swapped until it gets swapped again later.

You, Hyobin's best friend, have decided to help Hyobin, who is being tormented by the troublemaker Ukje. Help Hyobin compute $S$!

The first line gives $N$, the number of cows, and $Q$, the number of times Ukje will play his trick.

The second line gives the quality scores $A_i$ of the $N$ cows in order.

The third line gives the $Q$ cow indices $Q_i$ that Ukje will pick, in order.

Over $Q$ lines, print the recomputed value of $S$.

• $4 ≤ N ≤ 200\,000$
• $1 ≤ Q ≤ 200\,000$
• $1 ≤ |A_i| ≤ 10$
• $1 ≤ Q_i ≤ N$