Choosing Balls

给定一个长度为 $n$ 的球的序列，每个球有两个值 $c_i$ 和 $v_i$，分别表示颜色和价值。现在可以在序列中任意选出一个可能不连续的子序列（可能为空）。假设第 $i$ 个选中的球的编号为 $d_i$，则其对该子序列价值的贡献为： $$\begin{cases}a\times v_{d_i}&i\neq 1\text{且}c_{d_i}=c_{d_{i-1}}\\b\times v_{d_i}&\text{otherwise}\end{cases}$$ 定义空序列的价值为 $0$。 有 $q$ 次询问，每次询问指定一组新的 $a$ 和 $b$（在数据范围中第 $i$ 次询问指定的 $a$ 与 $b$ 分别记为 $a_i$ 与 $b_i$），求价值最大的子序列的价值。 **【数据范围】** $1\leq n\leq10^5$，$1\leq q\leq 500$，$1\leq c_i\leq n$，$|v_i|\leq 10^5$，$|a_i|,|b_i|\leq 10^5$。 注意 $v_i,a_i,b_i$ 均可能为负。

There are $ n $ balls. They are arranged in a row. Each ball has a color (for convenience an integer) and an integer value. The color of the $ i $ -th ball is $ c_{i} $ and the value of the $ i $ -th ball is $ v_{i} $ . Squirrel Liss chooses some balls and makes a new sequence without changing the relative order of the balls. She wants to maximize the value of this sequence. The value of the sequence is defined as the sum of following values for each ball (where $ a $ and $ b $ are given constants): - If the ball is not in the beginning of the sequence and the color of the ball is same as previous ball's color, add (the value of the ball) $ × $ $ a $ . - Otherwise, add (the value of the ball) $ × $ $ b $ . You are given $ q $ queries. Each query contains two integers $ a_{i} $ and $ b_{i} $ . For each query find the maximal value of the sequence she can make when $ a=a_{i} $ and $ b=b_{i} $ . Note that the new sequence can be empty, and the value of an empty sequence is defined as zero.

The first line contains two integers $ n $ and $ q $ ( $ 1<=n<=10^{5}; 1<=q<=500 $ ). The second line contains $ n $ integers: $ v_{1},v_{2},...,v_{n} $ ( $ |v_{i}|<=10^{5} $ ). The third line contains $ n $ integers: $ c_{1},c_{2},...,c_{n} $ ( $ 1<=c_{i}<=n $ ). The following $ q $ lines contain the values of the constants $ a $ and $ b $ for queries. The $ i $ -th of these lines contains two integers $ a_{i} $ and $ b_{i} $ ( $ |a_{i}|,|b_{i}|<=10^{5} $ ). In each line integers are separated by single spaces.

For each query, output a line containing an integer — the answer to the query. The $ i $ -th line contains the answer to the $ i $ -th query in the input order. Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

6 3
1 -2 3 4 0 -1
1 2 1 2 1 1
5 1
-2 1
1 0

20
9
4

4 1
-3 6 -1 2
1 2 3 1
1 -1

5

In the first example, to achieve the maximal value: - In the first query, you should select 1st, 3rd, and 4th ball. - In the second query, you should select 3rd, 4th, 5th and 6th ball. - In the third query, you should select 2nd and 4th ball. Note that there may be other ways to achieve the maximal value.