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.*;
import java.io.*;
public class Main {
    static class Scan {
        private byte[] buf=new byte[1024];
        private int index;
        private InputStream in;
        private int total;
        public Scan()
        {
            in=System.in;
        }
        public int scan()throws IOException
        {
            if(total<0)
            throw new InputMismatchException();
            if(index>=total)
            {
                index=0;
                total=in.read(buf);
                if(total<=0)
                return -1;
            }
            return buf[index++];
        }
        public int scanInt()throws IOException
        {
            int integer=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    integer*=10;
                    integer+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }
        public double scanDouble()throws IOException
        {
            double doub=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n)&&n!='.')
            {
                if(n>='0'&&n<='9')
                {
                    doub*=10;
                    doub+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            if(n=='.')
            {
                n=scan();
                double temp=1;
                while(!isWhiteSpace(n))
                {
                    if(n>='0'&&n<='9')
                    {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n=scan();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }
        public String scanString()throws IOException
        {
            StringBuilder sb=new StringBuilder();
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            while(!isWhiteSpace(n))
            {
                sb.append((char)n);
                n=scan();
            }
            return sb.toString();
        }
        private boolean isWhiteSpace(int n)
        {
            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
            return true;
            return false;
        }
    }
    
    public static void sort(int arr[],int l,int r) {    //sort(arr,0,n-1);
        if(l==r) {
            return;
        }
        int mid=(l+r)/2;
        sort(arr,l,mid);
        sort(arr,mid+1,r);
        merge(arr,l,mid,mid+1,r);
    }
    public static void merge(int arr[],int l1,int r1,int l2,int r2) {
        int tmp[]=new int[r2-l1+1];
        int indx1=l1,indx2=l2;
        //sorting the two halves using a tmp array
        for(int i=0;i<tmp.length;i++) {
            if(indx1>r1) {
                tmp[i]=arr[indx2];
                indx2++;
                continue;
            }
            if(indx2>r2) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            if(arr[indx1]<arr[indx2]) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            tmp[i]=arr[indx2];
            indx2++;
        }
        //Copying the elements of tmp into the main array
        for(int i=0,j=l1;i<tmp.length;i++,j++) {
            arr[j]=tmp[i];
        }
    }
    
    public static void sort(long arr[],int l,int r) {    //sort(arr,0,n-1);
        if(l==r) {
            return;
        }
        int mid=(l+r)/2;
        sort(arr,l,mid);
        sort(arr,mid+1,r);
        merge(arr,l,mid,mid+1,r);
    }
    public static void merge(long arr[],int l1,int r1,int l2,int r2) {
        long tmp[]=new long[r2-l1+1];
        int indx1=l1,indx2=l2;
        //sorting the two halves using a tmp array
        for(int i=0;i<tmp.length;i++) {
            if(indx1>r1) {
                tmp[i]=arr[indx2];
                indx2++;
                continue;
            }
            if(indx2>r2) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            if(arr[indx1]<arr[indx2]) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            tmp[i]=arr[indx2];
            indx2++;
        }
        //Copying the elements of tmp into the main array
        for(int i=0,j=l1;i<tmp.length;i++,j++) {
            arr[j]=tmp[i];
        }
    }
    
    
    
    static class seg_tree {
        long seg_tree[];
        public seg_tree(int n,long arr[]) {
            seg_tree=new long[4*n];
            create_seg_tree(arr,0,0,n-1);
        }

        //0 index-Left child-(2*i+1) Right Child-(2*i+2)

        public void create_seg_tree(long arr[],int vertex,int l,int r) {
            if(l==r) {
                seg_tree[vertex]=arr[r];
                return;
            }
            int mid=(l+r)/2;
            //Left Child
            create_seg_tree(arr,(2*vertex)+1,l,mid);
            //Right Child
            create_seg_tree(arr,(2*vertex)+2,mid+1,r);
            //Filling this node
            seg_tree[vertex]=Math.max(seg_tree[(2*vertex)+1],seg_tree[(2*vertex)+2]);
        }

        public long max(int vertex,int l,int r,int ql,int qr) {  //ql->query left , qr-> query right l->curr Segmrnt left    r->curr segment right
            if(ql>qr) {
                return 0;
            }

            if(ql==l && qr==r) {
                return seg_tree[vertex];
            }
            int mid=(l+r)/2;

            long max=Long.MIN_VALUE;

            //Left Child
            max=Math.max(max,max((2*vertex)+1,l,mid,ql,Math.min(qr, mid)));

            //Right Child
            max=Math.max(max,max((2*vertex)+2,mid+1,r,Math.max(mid+1,ql),qr));

            return max;
        }

        public void update(int vertex,int l,int r,int pos,long value) {   //pos->Position of the update   value->updates value
            if(l==r) {
                seg_tree[vertex]=value;
                return;
            }
            int mid=(l+r)/2;
            //Left Child
            if(pos<=mid) {
                update((2*vertex)+1,l,mid,pos,value);
            }
            //Right Child
            else {
                update((2*vertex)+2,mid+1,r,pos,value);
            }
            seg_tree[vertex]=Math.max(seg_tree[(2*vertex)+1],seg_tree[(2*vertex)+2]);
        }
    }

    
    
    
    
    
    
    
    
    
    public static void main(String args[]) throws IOException {
        Scan input=new Scan();
        StringBuilder ans=new StringBuilder("");
        int n=input.scanInt();
        int q=input.scanInt();
        long arr[]=new long[n];
        int clr[]=new int[n];
        for(int i=0;i<n;i++) {
            arr[i]=input.scanInt();
        }
        for(int i=0;i<n;i++) {
            clr[i]=input.scanInt()-1;
        }
        for(int qq=1;qq<=q;qq++) {
            int a=input.scanInt();
            int b=input.scanInt();
            ans.append(solve(n,arr,clr,a,b)+"\n");
        }
        System.out.println(ans);
    }
    public static long solve(int n,long arr[],int clr[],long a,long b) {
        long dp[]=new long[n];
        Arrays.fill(dp, Long.MIN_VALUE);
        long max=Long.MIN_VALUE,sec_max=Long.MIN_VALUE;
        int max_indx=-1,sec_max_indx=-1;
        for(int i=0;i<n;i++) {
            if(dp[clr[i]]!=Long.MIN_VALUE) {
                dp[clr[i]]=Math.max(dp[clr[i]],dp[clr[i]]+a*arr[i]);
            }
            dp[clr[i]]=Math.max(dp[clr[i]],b*arr[i]);
            if(max_indx!=-1 && max_indx!=clr[i]) {
                dp[clr[i]]=Math.max(dp[clr[i]],(b*arr[i])+max);
            }
            if(sec_max_indx!=-1 && sec_max_indx!=clr[i]) {
                dp[clr[i]]=Math.max(dp[clr[i]],(b*arr[i])+sec_max);
            }
            if(dp[clr[i]]>max) {
                if(max_indx==clr[i]) {
                    max=dp[clr[i]];
                    max_indx=clr[i];
                }
                else {
                    sec_max=max;
                    sec_max_indx=max_indx;
                    max=dp[clr[i]];
                    max_indx=clr[i];
                }
            }
            else if(dp[clr[i]]>sec_max && clr[i]!=max_indx) {
                sec_max=dp[clr[i]];
                sec_max_indx=clr[i];
            }
        }
        max=0;
        for(int i=0;i<n;i++) {
            max=Math.max(max,dp[i]);
        }
        return max;
    }
}