Your friend Mishka and you attend a calculus lecture. Lecture lasts n minutes. Lecturer tells ai theorems during the i-th minute.

Mishka is really interested in calculus, though it is so hard to stay awake for all the time of lecture. You are given an array t of Mishka's behavior. If Mishka is asleep during the i-th minute of the lecture then ti will be equal to 0, otherwise it will be equal to 1. When Mishka is awake he writes down all the theorems he is being told — ai during the i-th minute. Otherwise he writes nothing.

You know some secret technique to keep Mishka awake for k minutes straight. However you can use it only once. You can start using it at the beginning of any minute between 1 and n - k + 1. If you use it on some minute i then Mishka will be awake during minutes j such that <image> and will write down all the theorems lecturer tells.

You task is to calculate the maximum number of theorems Mishka will be able to write down if you use your technique only once to wake him up.

Input

The first line of the input contains two integer numbers n and k (1 ≤ k ≤ n ≤ 105) — the duration of the lecture in minutes and the number of minutes you can keep Mishka awake.

The second line of the input contains n integer numbers a1, a2, ... an (1 ≤ ai ≤ 104) — the number of theorems lecturer tells during the i-th minute.

The third line of the input contains n integer numbers t1, t2, ... tn (0 ≤ ti ≤ 1) — type of Mishka's behavior at the i-th minute of the lecture.

Output

Print only one integer — the maximum number of theorems Mishka will be able to write down if you use your technique only once to wake him up.

Example

Input

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


Output

16

Note

In the sample case the better way is to use the secret technique at the beginning of the third minute. Then the number of theorems Mishka will be able to write down will be equal to 16.
import java.io.*;
import java.util.*;

public class Solution {
	public final static int MOD = 1000000007;
	public static int count = 0;
	public static int dx[] = {-1,1,0,0};
	public static int dy[] = {0,0,-1,1};
	public static int max = 0;
	public static LinkedList<Integer> adj[];
	@SuppressWarnings("unchecked")
	public static void main(String[] args) throws IOException {
		InputReader scan = new InputReader(System.in);
	   	OutputStream outputStream = System.out;
	   	PrintWriter pw = new PrintWriter(outputStream);
	   	StringBuilder sb = new StringBuilder();
	   	int n = scan.nextInt();
	    int k = scan.nextInt();
	    int arr[] = new int[n];
	    for(int i=0;i<n;i++)
	    	arr[i] = scan.nextInt();
	    int t[] = new int[n];
	    for(int i=0;i<n;i++)
	    	t[i] = scan.nextInt();
	    int pre[] = new int[n-k+1];
	    for(int i=0;i<k;i++){
	    	if(t[i]==0)
	    		pre[0]+=arr[i];
	    }
	    int max = pre[0];
	    for(int i=k;i<n;i++)
	    {
	    	if(t[i-k]==0){
	    		pre[i-k+1] = pre[i-k]-arr[i-k];
	    	}
	    	else
	    		pre[i-k+1] = pre[i-k];
	    	if(t[i]==0)
	    		pre[i-k+1]+=arr[i];
	    	max = Math.max(pre[i-k+1], max);
	    }
	    for(int i=0;i<n;i++)
	    	if(t[i]==1)
	    		max+=arr[i];
	    pw.println(max);
	   	pw.close();  	
	}
	public static int find(int x,int parent[])
	{
		if(parent[x]!=x)
			parent[x] = find(parent[x],parent);
		return parent[x];
	}
	public static void union(int parent[],int x,int y)
	{
		int xParent = find(x,parent);
		int yParent = find(y,parent);
		parent[xParent] = yParent;
	}
	public static int dfs(int node,int parent,int arr[],int k)
	{
		int max = 0,sec_max = 0;
		for(int i=0;i<adj[node].size();i++)
		{
			if(adj[node].get(i)!=parent){
				int t = dfs(adj[node].get(i),node,arr,k);
				if(max<t)
				{
					sec_max = max;
					max = t;
				}
				else if(sec_max<t)
					sec_max = t;
			}
		}
		if(arr[node]%k==0){
			count = Math.max(count, sec_max+max+1);
			return sec_max+max+1;
		}
		else
			return 0;
	}
	static class Pair{
		int i,j,p;
		Pair(int a,int b,int parent)
		{
			i = a;
			j = b;
			p = parent;
		}
	}
	public static void buildTree(int arr[],int tree[],int node,int start,int end)
	{
		if(start==end)
		{
			tree[node] = arr[start];
			return;
		}
		int mid = (start+end)/2;
		buildTree(arr,tree,2*node,start,mid);
		buildTree(arr,tree,2*node+1,mid+1,end);
		tree[node] = tree[2*node]+tree[2*node+1];
	}
	public static void update(int arr[],int tree[],int node,int inx,int val,int start,int end)
	{ 
		if(start==end)
		{
			tree[node] = val;
			arr[inx] = val;
			return;
		}
		int mid = (start+end)/2;
		if(inx<=mid)
			update(arr,tree,2*node,inx,val,start,mid);
		else
			update(arr,tree,2*node+1,inx,val,mid+1,end);
		tree[node] = tree[2*node]+tree[2*node+1];
	}
	public static int query(int tree[],int node,int l,int r,int start,int end)
	{
		if(r<start || l>end)
			return 0;
		if(l<=start && end<=r)
			return tree[node];
		int mid = (start+end)/2;
		int ans1 = query(tree,2*node,l,r,start,mid);
		int ans2 = query(tree,2*node+1,l,r,mid+1,end);
		return ans1+ans2;
	}
	public static void merge(int arr[],int start,int mid,int end)
	{
		int l = start, r = mid+1;
		int temp[] = new int[end-start+1];
		int k = 0;
		for(int i=start;i<=end;i++)
		{
			if(l>mid)
				temp[k++] = arr[r++];
			else if(r>end)
				temp[k++] = arr[l++];
			else if(arr[l]<=arr[r])
				temp[k++] = arr[l++];
			else{
				temp[k++] = arr[r++];
				count+=(mid-l+1);
			}
		}
		for(int i=0;i<k;i++)
			arr[start++] = temp[i];
	}
	public static void mergeSort(int arr[],int l,int r)
	{
		if(l<r){
			int mid = (l+r)/2;
			mergeSort(arr,l,mid);
			mergeSort(arr,mid+1,r);
			merge(arr,l,mid,r);
		}
	}
	public static void sieve(int spf[],int n)
	{
		for(int i=1;i<=n;i++)
			spf[i] = i;
		for(int i=2;i*i<=n;i++)
		{
			if(spf[i]==i)
			{
				for(int j=i;j<=n;j+=i)
					if(spf[j]==j)
						spf[j] = i;
			}
		}
	}
	public static void factors(int n,int spf[],ArrayList<Integer> factors)
	{
		int pre = 0;
		while(n!=1)
		{
			int temp = spf[n];
			if(temp!=pre)
			{
				factors.add(temp);
				pre = temp;
			}
			n/=temp;
		}
	}
	public static boolean isPrime(int n)
	{
		if(n==0 || n==1)
			return false;
		int limit = (int)Math.sqrt(n);
		for(int i=2;i<=limit;i++)
		{
			if(n%i==0)
				return false;
		}
		return true;
	}
	public static long pow(long a,long b,int m)
	{
		long result = 1;
		while(b>0)
		{
			if(b%2==1)
				result = ((result%m)*(a%m))%m;
			a = ((a%m)*(a%m))%m;
			b/=2;
		}
		return result;
	}
	public static long mulinv(long a,long m)
	{
		long arr[] = new long[2];
		long gcd = gcdExtended(a,m,arr);
		if(gcd==1)
			return (arr[0]%m+m)%m;
		else
			return Integer.MAX_VALUE;
	}
	public static long gcdExtended(long a,long b,long arr[])
	{
		if (a == 0)
	    {
	        arr[0] = 0;
	        arr[1] = 1;
	        return b;
	    }
	    long gcd = gcdExtended(b%a, a, arr);
	    long temp = arr[0];
	    arr[0] = arr[1] - (b/a) * arr[0];
	    arr[1] = temp;
	    return gcd;
	}
	public static long kadane(int items[])
	{
		int n = items.length;
		long max = (long)items[0];
		long curr_max = (long)items[0];
		for(int i=1;i<n;i++)
		{
			curr_max = Math.max((long)curr_max+items[i], items[i]);
			max = Math.max(max, curr_max);
		}
		return max;
	}
	public static long gcd(int a,int b)
	{
		if(a%b==0){
			return pow(2,a-1,MOD);
		}
		long ans = gcd(b,a%b);
		int len = 0;
		long ans1 = 0;
		while(len<a)
		{
			if(a-len-b<0)
			{
				ans = ans>>(len+b-a);
				ans1 = (ans1+ans)%MOD;
			}
			else
				ans1 = (ans1+(ans*pow(2,a-b-len,MOD))%MOD)%MOD;
			len+=b;
		}
		System.out.println(ans1);
		return ans1;
	}
	public static int LCS(String s1,String s2) //Longest common subsequence
	{
		int n = s1.length();
		int m = s2.length();
		int lcs[][] = new int[n+1][m+1];
		for(int i=0;i<=n;i++)
		{
			for(int j=0;j<=m;j++)
			{
				if(i==0 || j==0)
					lcs[i][j] = 0;
				else if(s1.charAt(i-1)==s2.charAt(j-1))
					lcs[i][j] = lcs[i-1][j-1] + 1;
				else
					lcs[i][j] = Math.max(lcs[i][j-1], lcs[i-1][j]);
			}
		}
		return lcs[n][m];
	}
	static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}
class InputReader {
    public BufferedReader reader;
	public StringTokenizer tokenizer;
    public InputReader(InputStream inputstream) {
        reader = new BufferedReader(new InputStreamReader(inputstream));
		tokenizer = null;
	}
    public String nextLine(){
        String fullLine=null;
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
		    try {
		        fullLine=reader.readLine();
		    } catch (IOException e) {
    			throw new RuntimeException(e);
    			}
        		return fullLine;
        }
		return fullLine;
	}
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
    			tokenizer = new StringTokenizer(reader.readLine());
    		} catch (IOException e) {
        		throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
    public long nextLong() {
        return Long.parseLong(next());
	}
	public int nextInt() {
		return Integer.parseInt(next());
	}
}

class Node{
	int x, index;
	Node(int z,int y)
	{
		x = z;
		index = y;
	}
}
