Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Choosing Balls

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere 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.

Input

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.

Output

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.

Examples

Input

6 3

1 -2 3 4 0 -1

1 2 1 2 1 1

5 1

-2 1

1 0

Output

20

9

4

Input

4 1

-3 6 -1 2

1 2 3 1

1 -1

Output

5

Note

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.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/26/2017 12:15:05 (c4).

Desktop version, switch to mobile version.
User lists

Name |
---|