Problem: 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 ci and the value of the i-th ball is vi.

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 ai and bi. For each query find the maximal value of the sequence she can make when a = ai and b = bi.

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 ≤ 105; 1 ≤ q ≤ 500). The second line contains n integers: v1, v2, ..., vn (|vi| ≤ 105). The third line contains n integers: c1, c2, ..., cn (1 ≤ ci ≤ 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 ai and bi (|ai|, |bi| ≤ 105).

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.

Solution (in JAVA):

Solution:
import java.util.Scanner;
import java.io.OutputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author lgsmitty
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Scanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskE solver = new TaskE();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskE {
    public void solve(int testNumber, Scanner in, PrintWriter out) {

        final int MAXN = 100005;

        final int n = in.nextInt();
        int test = in.nextInt();

        final long value[] = new long[MAXN];
        final int color[] = new int[MAXN];

        for (int i = 0; i < n; ++i) {
            value[i] = in.nextLong();
        }

        for (int i = 0; i < n; ++i) {
            color[i] = in.nextInt();
        }


        final long maxValue[] = new long[MAXN];
        final int last[] = new int[MAXN];

        for (; test > 0; --test) {

            final long a = in.nextLong();
            final long b = in.nextLong();

            long f0value = 0;
            int f0color = -1;
            long f1value = 0;
            int f1color = -1;

            for (int i = 0; i < n; ++i) {

                final long v = value[i];
                final int c = color[i];

                long currentMaxValue = 0;

                if (f0color != -1) {
                    if (f0color != c) {
                        currentMaxValue = f0value;
                    } else if (f1color != -1) {
                        currentMaxValue = f1value;
                    }
                }

                if (last[c] != test) {
                    last[c] = test;
                    maxValue[c] = Math.max(currentMaxValue + b * v, b * v);

                    if (f0color == -1) {
                        f0color = c;
                        f0value = maxValue[c];
                    } else if (maxValue[c] > f0value) {
                        if (f1color == -1) {
                            if (c != f0color) {
                                f1value = f0value;
                                f1color = f0color;
                            }
                        }
                        else if (c == f0color) {
                        } else if (c == f1color) {
                            f1value = f0value;
                            f1color = f0color;
                        } else {
                            f1value = f0value;
                            f1color = f0color;
                        }

                        f0color = c;
                        f0value = maxValue[c];
                    }
                    else if (maxValue[c] > f1value || f1color == -1){

                        if (c != f0color){
                            f1color = c;
                            f1value = maxValue[c];
                        }
                    }

                    continue;
                }

                final long vb = Math.max(currentMaxValue + b * v, b * v);
                final long va = maxValue[c] + a * v;

                maxValue[c] = Math.max(maxValue[c], Math.max(va, vb));


                if (f0color == -1) {
                    f0color = c;
                    f0value = maxValue[c];
                } else if (maxValue[c] > f0value) {
                    if (f1color == -1) {
                        if (c != f0color) {
                            f1value = f0value;
                            f1color = f0color;
                        }
                    }
                    else if (c == f0color) {
                    } else if (c == f1color) {
                        f1value = f0value;
                        f1color = f0color;
                    } else {
                        f1value = f0value;
                        f1color = f0color;
                    }

                    f0color = c;
                    f0value = maxValue[c];
                }
                else if (maxValue[c] > f1value || f1color == -1){

                    if (c != f0color){
                        f1color = c;
                        f1value = maxValue[c];
                    }
                }
            }

            long result = 0;
            for (int i = 0; i < MAXN; ++i) {
                if (last[i] == test) {
                    if (maxValue[i] > result) {
                        result = maxValue[i];
                    }
                }
            }

            out.println(result);
        }
    }
}